Module 3.Lesson 2.Practice.KEY PDF

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Module 3: Lesson 2

Practice

1. The height of all 3-year-old females is approximately normally distributed with μ = 38.72 inches and σ = 3.17 inches. What is the probability that a random sample of ten 3-year-old females result in a sample mean greater than 40 inches? n=10

  38.72

  3.17

x  40

x 

3.17

 1.002

10

40

z

40 38.72  1.28 1.002

Z-Table → 0.8997

1 – 0.8997 = 0.1003

10.03% chance that a sample of ten 3-year-old females will have a mean height greater than 40 inches.

2. A manufacturer of flashlight batteries claims that its batteries will last an average of µ = 34 hours of continuous use. Of course, there is some variability in life expectancy with σ = 3 hours. During consumer testing, a sample of 30 batteries lasted an average of only 32.5 hours. How likely is it to obtain a sample that performs this badly if the manufacturer’s claim is true? n=30  3 x  32.5   34

x 

3  0.55 30

32.5

z

32.5  34   2.73 0.55

Z-Table → 0.0032

There is a 0.32% chance that a sample mean lifetime of 30 batteries will last only 32.5 hours.

3. For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 25 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122.  114.8 n=25 x 119 and x 122  13.1

x 

13.1

119

z

122  114.8  2.77 2.6

Z-Table → 0.9972

z

119  114.8  1.62 2.6

Z-Table → 0.9474

 2.6

25

122

0.9972 - 0.9474 = 0.0498 There is a 4.98% chance that a sample of 25 women will have a mean systolic blood pressure between 119 mm Hg and 122 mm Hg....