web view... chapter 5. stats: modeling the world – chapter 5. 24. ap statistics . chp 1-2...

AP STATISTICS Chp 1-2 Packet

_______ Page 2 Warm Ups _______ Page 6 Chp 1- 2 Chapter Outline_______ Page 8 M&M Data Collection _______ Page 9 Chp 2 Class Notes_______ 1 Chp 2 Group Quiz_______ Page 12 Chp 3 Chapter Outline_______ Page 14 Chp 3 Class Notes_______ Page 20 Chp 3 Classwork Smoking and Education_______ Page 21 Chp 3 Group Quiz_______ Page 22 Chp 3 Investigative Task

_______ Page 25 Chp 4 Outline_______ Page 27 Chp 4 Class Notes_______ Page 31 Chp 4 Investigative Task_______ Page 34 Chp 4 Group Quiz_______ Page 35 Chp 5 Chapter Outline

_______ Page 37 Chp 5 Class Notes _______ Page 39 Chp 5 Mooseburgers and McTofu_______ Page 40 Chp 5 Investigative Task Auto Safety_______ Page 43 Chp 5 Group Quiz

_______ Page 45 Chp 6 Outline_______ Page 48 Chp 6 Notes_______ Page 52 Chp 6 Investigative Task_______ Page 55 Chp 6 Group Quiz

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Warm Ups:p.17 #15

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Warm Ups: (cont)

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Chapter Outlinep. 43 #38

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Chapter 1: Stats Starts HereChapter 2: Data1. Name three things you learned about Statistics in Chapter 1.

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2. The authors claim that this book is very different from a typical mathematics textbook.Would you agree or disagree, based on what you read in Chapter 1? Explain.

3. According to the authors, what are the “three simple steps to doing Statistics right?”

4. What do the authors refer to as the “W’s of data?”

5. Why must data be in context (the W’s)?

6. Explain the difference between a categorical variable and a quantitative variable. Give an example of each.

Key Vocabulary:Statistics_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ƒ data, datum _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ƒ variation

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_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

ƒ individual______________________________________________________________________________________________________________________________________________________________________ƒ respondent______________________________________________________________________________________________________________________________________________________________________

ƒ subject________________________________________________________________________________________________________________________________________________________________________

ƒ participant________________________________________________________________________________________________________________________________________________________________________ƒ experimental unit________________________________________________________________________________________________________________________________________________________________________ƒ observation________________________________________________________________________________________________________________________________________________________________________ƒ variable________________________________________________________________________________________________________________________________________________________________________

ƒ categorical________________________________________________________________________________________________________________________________________________________________________

ƒ quantitative______________________________________________________________________________________________________________________________________________________________________Calculator Skills:enter data in a list______________________________________________________________________________________________________________________________________________________________________change a datum______________________________________________________________________________________________________________________________________________________________________delete a datum

___________________________________________________________________________________name a new list

___________________________________________________________________________________clear a list

_____________________________________________________________________________________delete a list

____________________________________________________________________________________

recreate a list____________________________________________________________________________________

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copy a list____________________________________________________________________________________

Class notes Chapter 2: Data

What are data?

In order to determine the context of data, consider the “W’s”

Who –

What (and in what units) –

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When –

Where –

Why –

How –

There are two major ways to treat data:

A _______________ _______________ is used to answer questions about how cases fall into categories. A categorical variable may be comprised of word labels, or it may use numbers as labels.

Examples:

A _______________ _______________ is used to answer questions about the quantity of what is being measured. A quantitative variable is comprised of numeric values.

Examples:

What is a statistic?

Are the numbers 17, 21, 44, 76 data?

Data must have ______ to be meaningful. The numbers listed above could be test scores, ages of a group of golfers, or the uniform numbers of the starting backfield on the football team. Without ______ data cannot be interpreted.

Suppose a Consumer Reports article (published in June 2005) on energy bars gave the brand name, flavor, price, number of calories, and grams of protein and fat. Identify the following:

Who:

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What:

When:

Where:

How:

Why:

Categorical variables:

Quantitative variables (with units):

A report on the Boston Marathon listed each runner’s gender, county, age, and time. Identify the following:

Who:

What:

When:

Where:

How:

Why:

Categorical variables:

Quantitative variables (with units):

Chp 1-2 Quiz

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Chapter OutlineChapter 3: Displaying and DescribingCategorical Data

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1. According to the authors, what are the three rules of data analysis?

2. Explain the difference between a frequency table and a relative frequency table.

3. When is it appropriate to use a bar chart?

4. When is it appropriate to use a pie chart?

5. When is it appropriate to use a contingency table?

6. What does a marginal distribution show?

7. When is it appropriate to look at a conditional distribution?

8. What does it mean for two variables to be independent?

9. How does a segmented bar chart compare to a pie chart?

10. Explain what is meant by Simpson’s Paradox.

Key Vocabulary:

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ƒ frequency table__________________________________________________________________________________________________________________________________________________________________________ƒ relative frequency table__________________________________________________________________________________________________________________________________________________________________________

ƒ distribution__________________________________________________________________________________________________________________________________________________________________________

ƒ bar chart__________________________________________________________________________________________________________________________________________________________________________

ƒ pie chart__________________________________________________________________________________________________________________________________________________________________________ƒ contingency table__________________________________________________________________________________________________________________________________________________________________________

ƒ marginal distribution__________________________________________________________________________________________________________________________________________________________________________

ƒ conditional distribution__________________________________________________________________________________________________________________________________________________________________________

ƒ independent__________________________________________________________________________________________________________________________________________________________________________

ƒ segmented bar chart__________________________________________________________________________________________________________________________________________________________________________

Simpson’s Paradox__________________________________________________________________________________________________________________________________________________________________________

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Stats: Modeling the World – Chapter 5

Chapter 3 – Displaying and Describing Categorical Data

_______________ _______________ are often used to organize categorical data. Frequency tables display the category names and the _______________ of the number of data values in each category. _ _______________________ also display the category names, but they give the _______________ rather than the counts for each category.

Color Freq. Rel. Freq. Percent

Blue 13

Red 7

Orange 11

Green 9

Yellow 8

Brown 7

TOTAL 55 1.000 100%

A _______________ is often used to display categorical data. The height of each bar represents the _______________ for each category. Bars are displayed next to each other for easy comparison. When constructing a bar chart, note that the bars do not _______________ one another. Categorical variables usually cannot be ordered in a meaningful way; therefore the order in which the bars are displayed is often meaningless.

A _________ bar chart displays the proportion of counts for each category.

Blue Red Orange Green Yellow Brown

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2

4

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8

10

12

14 13

7

11

98

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M&M Color Distribution

Freq

uenc

y


The sum of the relative frequencies is _____.

A _______________ _______________ is another type of display used to show categorical data. Pie charts show parts of a whole. Pie charts are often difficult to construct by hand.

A _______________ _______________ shows two categorical variables together. The margins give the frequency distributions for each of the variables, also called the ________ ___ .

Examine the class data about gender and political view – liberal, moderate, conservative.

Liberal Moderate Conservative TOTAL

Male

Female

TOTAL

What percent of the class are girls with liberal political views?

What percent of the liberals are girls?

What percent of the girls are liberals?

What is the marginal distribution of gender?

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Blue Red Orange Green Yellow Brown

0%

5%

10%

15%

20%

25%

30%24%

13%

20%16%

14% 13%

M&M Color DistributionFr

eque

ncy


What is the marginal distribution of political views?

A conditional distribution shows the distribution of one variable for only the individuals who satisfy some condition on another variable.

The conditional distribution of political preference, conditional on being male:


Male

The conditional distribution of political preference, conditional on being female:


Female

What is the conditional relative frequency distribution of gender among conservatives?

If the conditional distributions are the same, we can conclude that the variables are not associated. Therefore, they are _______________ of one another.

If the conditional distributions differ, we can conclude that the variables are somehow associated. Therefore, they are _______________ of one another.

Are gender and political view independent?

A segmented bar chart displays the same information as a pie chart, but in the form of bars instead of circles. Comparing segmented bar charts is a good way to tell if two variables are independent of one another or not.

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Male Female0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Gender vs. Political Preference

Perc

ent

Explain how the graph on the left violates the “area principle.”

Explain what is wrong with the graph below.

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Averaging one variable across different levels of a second variable can lead to ______________________________. Consider the following example:

It’s the last inning of an important game. Your team is a run down with the bases loaded and two outs. The pitcher is due up, so you’ll be sending in a pinch-hitter. There are 2 batters available on the bench. Whom should you send in to bat?

Player Overall

A 33 for 103

B 45 for 151

Compare A’s batting average to B’s batting average. Which player appears to be the better choice?

Does it matter whether the pitcher throws right- or left-handed?

Player Overall vs LHP vs RHP

A 33 for 103 28 for 81 5 for 22

B 45 for 151 12 for 32 33 for 119

Compare A’s batting average vs. a left-handed pitcher to B’s. Compare A’s batting average against a right-handed pitcher. Which player appears to be the better choice?

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Pooling the data together loses important information and sometimes leads to the wrong conclusion. We always should take into account any factor that might matter.

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Group Quiz Chp 3

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Chp 3 Investigative Task

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Investigative Task Answer:

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Investigative Task Rubric

Chp 4 Outline: Displaying Quantitative Data24


1. What is meant by a distribution?

2. Explain the difference between a histogram and a relative frequency histogram.

3. In what ways are histograms similar to stem-and-leaf displays?

4. Name some advantages and disadvantages of stem-and-leaf displays.

5. When is it more appropriate to use a histogram rather than a stem-and-leaf display?

6. Name some advantages and disadvantages of dotplots.

7. When describing a distribution, what three things should you always mention?

8. What should you look for when describing the shape of a distribution?

9. In general, what is meant by the center of a distribution?

10. In general, what is meant by the spread of a distribution?

11. When is it appropriate to use a time plot to display quantitative data?

12. What is meant by re-expressing or transforming data? What is the purpose of re-expressingor transforming data?

Key Vocabulary:Distribution

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histogram

relative frequency

histogram

stem-and-leaf display

dotplot

shape

center

spread

mode

unimodal

bimodal

multimodal

uniform

SymmetricTail

skewed

outliers

gaps

time plot

re-expressing data

Calculator Skills:

display a histogram Sort A( ƒ

display a histogram ƒ

ƒƒƒƒƒƒƒ

Chp 4 Notes: Displaying Quantitative Data

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A _______________ or _______________ is often used to display categorical data. These types of displays, however, are not appropriate for quantitative data. Quantitative data is often displayed using either a _______________ _______________ or a _______________

In a histogram, the interval corresponding to the width of each bar is called a _______________ A histogram displays the bin counts as the height of the bars (like a bar chart). Unlike a bar chart, however, the bars in a histogram _______________ one another. An empty space between bars represents a _______________ in data values. If a value falls on the border between two consecutive bars, it is placed in the bin on the _______________.

6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13

Shoe Sizes of AP Stat Students

Shoe Size

# of

Stu

dent

s

A _______________ _______________ histogram displays the proportion of cases in each bin instead of the count.

Histograms are useful when _____________________________________________, and they can easily be constructed using a graphing calculator. A disadvantage of histograms is that they _______________ ______________________________.

Be sure to choose an appropriate bin width when constructing a histogram. As a general rule of thumb, your histogram should contain about _______ bars.

A _______________ _______________ is similar to a histogram, but it shows_______________ _______________ rather than bars. It may be necessary to _______________ stems if the range of data values is small.

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Number of Pairs of Shoes Owned

0

0

1

1

2

2

3

3

KEY:

A _______________ _______________ stem-and-leaf plot can be useful when _______________ two distributions.

Number of Pairs of Shoes Owned

Male Female .

0

0

1

1

2

2

3

3

KEY:

The stems of the stem-and-leaf plot correspond to the _______________ of a histogram. You may only use ______ digit for the leaves. Round or truncate your values if necessary.

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Stem-and-leaf plots are useful when working with sets of data that are __________________ __________________ in size, and when you want to display _______________ _______________.

How would you setup the following stem-and-leaf plots?

quiz scores (out of 100)

student GPA’s

student weights

SAT scores

weights of cattle (1000-2000 pounds)

_____________ may also be used to display quantitative variables. Dot plots are useful when working with ____________ sets of data.

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Guess Your Teacher's Age

Predicted Age

When describing a distribution, you should tell about three things: _______________ , _______________, and _______________. You should also mention any unusual features, like _______________ or _______________.

Identify the shapes of the following distributions:

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When comparing two or more distributions, compare the _______________ , _______________, and _______________, and compare any _______________ features. It is important, when comparing distributions, that their graphs be constructed using the same _______________.

You can sometimes make a skewed distribution appear more symmetric by _______________ (or transforming) your data.

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Chp 4 Investigative Task (Like #6 on AP test)


______________________________________________________________________________________________________________________________________

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________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Investigative Task Rubric:

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Chapter 4 Group Quiz

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Chapter Outline 5: Describing Distributions Numerically

1. Explain the difference between range and interquartile range. Why is the interquartile range often a better measure of the spread of a distribution?

2. What are some advantages of boxplots?

3. What are some disadvantages of boxplots?

4. When is it more appropriate to use the mean as a measure of center rather than the median?Why?

5. When is it more appropriate to use the median as a measure of center rather than the mean?Why?

6. When do the mean and median have the same value?

7. Describe the relationship between variance and standard deviation.

Key VocabularyCenter

ƒ spread

ƒ midrange

ƒ median

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ƒ range

36


ƒ quartile

ƒ interquartile range

ƒ percentile

ƒ five-number summary

ƒ boxplot

Calculator Skills:Boxplot

Modified boxplot

1 Var Stats

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Chp 6 Notes: Describing Distributions Numerically

When describing distributions, we need to discuss _______________, _______________, and _______________. How we measure the center and spread of a distribution depends on its _______________. The center of a distribution is a “typical” value. If the shape is unimodal and symmetric, a “typical” value is in the _______________. If the shape is skewed, however, a “typical” value is not necessarily in the middle.

For _______________ distributions, use the _______________ to determine the _______________ of the distribution and the _______________ to describe the _______________ of the distribution.

The median:

is the _______________ data value (when the data have been _______________) that divides the histogram into two equal _______________

has the same _______________ as the data

is _______________ to outliers (extreme data values)

The range:

is the difference between the _______________ value and the _______________ value

is a _______________, NOT an _______________

is _ ___ to outliers

The interquartile range (IQR):

contains the _______________ of the data

is the difference between the _______________ and _______________ quartiles

is a _______________, NOT an _______________

is _______________ to outliers

The _______________ _______________ gives: _______________, _______________, _______________, _______________, _______________,

A graphical display of the five-number summary is called a _______________.

How many hours, on average, do you spend watching TV per week? ______ Collect data from the entire class and record the values in order from smallest to largest. Calculate the five-number summary:

Construct both a histogram and a boxplot (using the same scale). Compare the displays.

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Average Number of Hours per Week Spent Watching TV

For _______________ distributions, use the _________________ _to determine the _______________ of the distribution and the _______________ to describe the _______________ of the distribution.

The mean:

is the arithmetic _______________ of the data values

is the ____ _ of a histogram

has the same _______________ as the data

is _______________ to outliers

is given by the formula

The standard deviation:

measures the “typical” distance each data value is from the _______________

Because some values are above the mean and some are below the mean, finding the sum is not useful (positives cancel out negatives); therefore we first _______________ the deviations, then calculate an _______________ _______________ . This is called the _______________. This statistics does not have the same units as the data, since we squared the deviations. Therefore, the final step is to take the _______________ of the variance, which gives us the _______________ .

is given by the formula

is _______________ _ to outliers, since its calculation involves the _______________

Find the mean and standard deviation of the average number of hours spent watching TV per week for this class.

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Stats: Modeling the World – Chapter 5Classwork Chp 5

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Investigative Task Auto Safety

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Stats: Modeling the World – Chapter 5Investigative Task Answer:

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Investigative Task Rubric:

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Chp 5 Group Quiz

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Chapter Outline 6: The Standard Deviationas a Ruler and the Normal Model1. What unit of measurement is used to describe how far a set of values are from the mean?

2. Explain how to standardize a value.

3. Briefly describe why standardized units are used to compare values that are measured using different scales, different units, or different populations.

4. How does adding or subtracting a constant amount to each value in a set of data affect the mean? Why does this happen?

5. How does multiplying or dividing a constant amount by each value in a set of data (also called rescaling) affect the mean? Why does this happen?

6. How does adding or subtracting a constant amount to each value in a set of data affect the standard deviation? Why does this happen?

7. How does multiplying or dividing a constant amount by each value in a set of data (also called rescaling) affect the standard deviation? Why does this happen?

8. How does standardizing a variable affect the shape, center, and spread of its distribution?

9. In what way does a z-score give an indication of how unusual a value is?

10. How would you describe the shape of a normal curve? Draw several examples.

11. Where on the normal curve are inflection points located?

12. When is it appropriate to use a normal model to model a set of data?

13. Explain the difference between y and μ .

14. Explain the difference between s and σ .

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15. Briefly explain the 68-95-99.7 Rule.

16. What is a percentile?

17. Is there a difference between the 80th percentile and the top 80%? Explain.

18. Describe two methods for assessing whether or not a distribution is approximately normal.

Key Vocabularystandard deviation _____________________________________________________________________________________

standardized value_____________________________________________________________________________________rescaling_____________________________________________________________________________________z-score_____________________________________________________________________________________normal model___________________________________________________________________________________

parameter_____________________________________________________________________________________statistic_____________________________________________________________________________________standard Normal model_____________________________________________________________________________________68-95-99.7 Rule_____________________________________________________________________________________normal probability plot

Calculator Skills:normalpdf(_____________________________________________________________________________________

normalcdf(

_____________________________________________________________________________________invNorm(_____________________________________________________________________________________normal probability plot_____________________________________________________________________________________-1E99 and 1E99__________________________________________________________________________________________________________________________________________________________________________

N( μ , σ )

_____________________________________________________________________________________

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Chapter 6: Normal Percentiles

1. Suppose the class took a 40-point quiz. Results show that a mean score of 30, median 32, IQR 8, standard deviation 6, min 12 and lower quartile 27. You got a 35. What happens to each of the statistics if…

a. I decide to weight the quiz as 50 points by adding 10 points to each score. Your score is now 45.

= M =

IQR = s =

min = Q1=

b. I decide to weight the quiz as 80 points by doubling each score. Your score is now 70.= M =

IQR = s =

min = Q1=

c. I decide to count the quiz as 100 points by doubling each score, then adding 20 points. Your score is now 90.

= M =

IQR = s =

min = Q1=

2. Consider the three athletes’ performances shown below in a 3-event competition. Note that each person finishes first, second, and third one time. Who deserves the gold medal? And who gave the most remarkable performance of the competition?

EventCompetitor 100 m Dash Shot Put Long Jump

A 10.1 sec 66’ 26’B 9.9 sec 60’ 27’C 10.3 sec 63’ 27’ 3”

Mean 10 sec 60’ 26’St Dev 0.2 sec 3’ 6”

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3. Sketch a Normal model for each of the following:a. Birthweights of babies, N(7.6 lb, 1.3 lb)

b. ACT scores at a certain college N(21.2, 4.4)

4. Use your knowledge of Normal models to guess plausible standard deviations for each of the following variables.

a. Height of 16-yr old girls

b. Weight of high school boys

c. Current price of gasoline

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5. Suppose a Normal model describes the fuel efficiency of cars currently registered in Maryland. The mean is 24 mpg, with a standard deviation of 6 mpg.

a. Sketch the Normal model.

b. What percent of all cars get less than 15 mpg?

c. What percent of all cars get between 20 and 30 mpg?

d. What percent of cars get more than 40 mpg?

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e. Describe the fuel efficiency of the worst 20% of all cars.

f. What gas mileage represents the third quartile?

g. Describe the gas mileage of the most efficient 5% of all cars.

h. An ecology group is lobbying for a national goal calling for no more than 10% of all cars to be less than 20 mpg. If the standard deviation does not change what average fuel efficiency must be attained?

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______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Group Quiz Chp 6

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