Unit 4 – Probability and Statistics

Section 12.7

Day 10

Warm-UpUsing the given data set:

77, 76, 83, 88, 90, 85, 81, 77, 95, 89

1. Find the mean, median, mode

2. Find the range and interquartile range

3. Create a box-and-whisker plot of the data

4. Find the standard deviation (Show all your work.)

Warm-Up AnswersData set in order:

76, 77, 77, 81, 83, 85, 88, 89, 90, 95

1. Mean = 84.1; Median = 84 ; Mode = 77

2. Range = 19; Interquartile range = 12

3. Create a box-and-whisker plot of the data

4. Standard deviation σ = 6.1

Section 12.7 Normal DistributionsGoal: calculate probabilities using normal distributions

Normal Curve – symmetrical bell-shaped curve

Important symbols σ (Sigma) represents standard deviation x (x-bar) represents mean

Section 12.7 Normal DistributionsImportant Aspects of a Normal Curve

Total Area under the curve is 168% of the area lies within 1 standard deviation

of the mean95% of the area lies within 2 standard deviations

of the mean99.7% of the area lies within 3 standard

deviations of the mean

Section 12.7 Normal Distributions

x +σ +2σ +3σ-σ-2σ-3σ

34%34%

13.5%

2.35% 2.35%

13.5%0.15%0.15%

Example 1The price of sandals is normally distributed with a

mean of $36 and a standard deviation of $9.

A) What percent were priced between $18 and $72?

B) What is the probability that a randomly chosen pair is priced between $9 and $18?

Example 1 (cont.)

$36 $45 $54 $63$27$18$9

34%34%

13.5%

2.35% 2.35%

13.5%0.15%0.15%

A) What percent were priced between $18 and $72?97.5%

Example 1 (cont.)

$36 $45 $54 $63$27$18$9

34%34%

13.5%

2.35% 2.35%

13.5%0.15%0.15%

B) What is the probability that a randomly chosen pair is priced between $9 and $18? 2.35%

Example 2The weight of strawberries packed in a medium-sized container

was normally distributed with a mean of 16.18 ounces and a standard deviation of 0.34 ounce.

A) If you randomly choose 2 containers of strawberries, what is the probability that both weigh less than 15.5 ounces?

B) If you randomly choose 2 containers of strawberries, What is the probability that both of the containers weighs at least 15.84 ounces?

C) If you randomly choose 2 containers of strawberries, that one container weighs between 15.5 and 15.84 ounces, and the 2nd container weighs at least 16.86 ounces?

Example 2 (cont.)

16.18 16.52 16.86 17.215.8415.515.16

34%34%

13.5%

2.35% 2.35%

13.5%0.15%0.15%

(oz.)

A) Both containers weigh less than 15.5 oz?0.025 0.025 = 0.000625 or 0.0625%

Example 2 (cont.)

16.18 16.52 16.86 17.215.8415.515.16

34%34%

13.5%

2.35% 2.35%

13.5%0.15%0.15%

(oz.)

B) Both containers weigh at least 15.84 oz?0.84 0.84 = 0.7056 or 70.56%

Example 2 (cont.)

16.18 16.52 16.86 17.215.8415.515.16

34%34%

13.5%

2.35% 2.35%

13.5%0.15%0.15%

(oz.)

C) Between 15.5 and 15.84 oz and at least 16.86?0.135 (0.0235 + .0015) = 0.003375 or 0.3375%

PRACTICE

P. 749-750

#19 - 28

PRACTICE ANSWERS19) 50%

20) 15.85%

21) 2.5%

22) 27%

23) 0.68

24) 0.4985

25) 0.9735

26) 0.84

27) 0.84

28) 0.975

HOMEWORK

P. 750-751

#29 – 31, 38 - 49