Q. T7.4 The central limit theorem is imp... [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. T7.4 (page 486)

The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the
a. sample size is reasonably large (for any population).
b. population is Normally distributed (for any sample size).
c. population is Normally distributed and the sample size is reasonably large.
d. population is Normally distributed and the population standard deviation is known (for any sample size).
e. population size is reasonably large (whether the population distribution is known or not).

Short Answer

Expert verified

(a) The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the sample size is reasonably large (for any population).

Step by step solution

Given Information

The central limit theorem is significant in statistics because it allows us to find probabilities involving the sample mean using a Normal distribution.

Explanation for correct option

According to the central limit theorem, if the sample size is big, the sampling distribution of the sample mean $\overset{炉}{x}$ is approximately normal.

As a result, the best solution is (a)