unit 4 – probability and statistics section 12.7 day 10
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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
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