Q. 76 The number of hours a lightbulb ... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 7: Q. 76 (page 481)

The number of hours a lightbulb burns before failing varies from bulb to bulb. The population distribution of burnout times is strongly skewed to the right. The central limit theorem says that
a. as we look at more and more bulbs, their average burnout time gets ever closer to the mean $渭$ for all bulbs of this type.
b. the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution.
c. the average burnout time of a large number of bulbs has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.
d. the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.
e. the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal.

Short Answer

Expert verified

(d). the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal.

Step by step solution

Given Information

The amount of time a lightbulb lasts before it burns out varies from bulb to bulb. Burnout times are heavily biassed to the right across the population.

Explanation for correct option

If the sample size is higher than or equal to 30, the sampling distribution of the sample mean will be nearly normal with mean and standard deviation, $蟽 / \sqrt{n}$ according to the central limit theorem.

Therefore, the correct option is (d)

Explanation for incorrect option

a. as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type is not the correct answer

b. the average burnout time of a large number of bulbs has a sampling distribution with the same shape (strongly skewed) as the population distribution is not the correct answer

c. the average burnout time of a large number of bulbs has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution is not the correct answer.

d. the average burnout time of a large number of bulbs has a sampling distribution that is close to Normal is not the correct answer

e. the average burnout time of a large number of bulbs has a sampling distribution that is exactly Normal is not the correct answer