WARM UP An unbiased coin is tossed 6 times. Our goal when

tossing a coin is to get heads. Calculate:

1. At least 3 heads

2. At most 2 heads.

MORE EXAMPLES FOR AREA Find the area/probability of the following:

Left of z = -2.50P(z < -2.5)

Right of z = - 1.20P(z > -1.2)

EVEN MORE EXAMPLES FOR AREAFind the area/probability of the following:

P(0 < z < 2.32)

P(-1.2 < z < 2.3)

AND ONE MORE EXAMPLE FOR AREAFind the area/probability of the following:

P(z < -3.01 and z > 2.43)

APPLICATION 1 A Calculus exam is given to 500 students.

The scores have a normal distribution with a mean of 78 and a standard deviation of 5. What percent of the students have scores between 82 and 90? How many students have scores between 82 and 90?

APPLICATION 2 A Calculus exam is given to 500 students.

The scores have a normal distribution with a mean of 78 and a standard deviation of 5. What percent of the students have scores above 70? How many students scored above a 70?

APPLICATION 3 Find the probability of scoring below a

1400 on the SAT if the scores are normal distributed with a mean of 1500 and a standard deviation of 200.

FINDING Z-SCORES FROM AREA Find the z-score above the mean with an

area to the left of z equal to 0.9325

Find the z-score below the mean with an area to the left of z equal to 13.87%

WARM-UP1. Find the percentage of the given z-score.

a) z is less than -0.47 b) z is greater than 0.54

c) z is less than 2.03 d) z is greater than 1.16

2. Find the percentage of the given z-score.

a) Z is between -2.05 and 0.78 b) z is between -1.11 an -0.32

MORE FINDING Z-SCORES FROM AREA Find the z-score below the mean with an

area between 0 and z equal to 0.4066

EVEN MORE FINDING Z-SCORES FROM AREA

Find the z-score above the mean with an area between 0 and z equal to 0.2123

Find the z to the right of the mean with an area to the right of z equal to 0.0239

INVERSE NORMAL DISTRIBUTIONS Find k for which P(x < k) = 0.95 given that x is normally

distributed with a mean of 70 and a standard deviation of 10.

SKIP

APPLICATIONS A professor determines that 80% of this year’s History

candidates should pass the final exam. The results are expected to be normally distributed with a mean of 62 and standard deviation of 13. Find the lowest score necessary to pass the exam.

MORE APPLICATIONS Researchers want to select people in the middle 60% of

the population based on their blood pressure. If the mean is 120 and the S.D. is 8. Find the upper and lower reading that would qualify.

FINDING STATS BASED ON PROBABILITY

Sacks of potatoes with a mean weight of 5 kg are packed by an automatic loader. In a test, it was found that 10% of bags were over 5.2 kg. Use this information to find the standard deviation of the process

MORE FINDING STATS BASED ON PROBABILITY

Find the mean and the standard deviation of a normally distributed random variables X, if P(x > 50) = 0.2 and P(x < 20) = 0.3

SKIP

MEASURING LOCATION IN A DISTRIBUTION

Draw a dotplot for class data, displaying the height of students in a class.

The pth percentile of a distribution is the value with p percent of the observations less than or equal to it.

Percentiles separate data sets into 100 equal parts. The percentile rank of a data value is the percentage of data values that are less than or equal to that value.

1. For Brett, who is 74 inches tall, find his percentile rank?

2. For Ms. Watts, who is 69 inches tall, find her percentile rank?

3. When the heights of 250 9th grade boys were measured, Jaden found that his height placed him at the 82nd percentile. Which of the following gives the number of boys that were at or below Jaden’s height?

(A) 82 (B) 28

(C) 45 (D) 205

4. Landon took a competitive spelling test with 600 other area students. When the results were announced, Landon found out he scored in the 93rd percentile. Which of the following gives the number of students who did better on the spelling test than Landon?

(A) 7 (B) 65

(C) 93 (D) 42

5. The following box-and-whiskers diagram gives the results on a recent SAT math test.(a) What is the 25th percentile score?

(b) What is the 50th percentile score?

(c) What is the 75th percentile score?

(d) What is the 100th percentile score?