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Chapter 7: Q 7.66. (page 307)

According to the central limit theorem, for a relatively large sample size, the variable x~is approximately normally distributed.

a. What rule of thumb is used for deciding whether the sample size is relatively large?

b. Roughly speaking, what property of the distribution of the variable under consideration determines how large the sample size must be for a normal distribution to provide an adequate approximation to the distribution of x~ ?

Short Answer

Expert verified

Part (a)the sample size is greater than30.

Part (b) For a normal distribution to provide an adequate approximation to the distribution of x炉the sample size must be large.

Step by step solution

01

Part (a) Step 1: Given information 

the variablex~is approximately normally distributed.

02

Part (a) Step 2: Concept

Formula used:population mean and standard deviation:渭x炉=渭and蟽x炉=蟽/n.

03

Part (a) Step 3: Explanation

We consider a sample as a large sample if the sample size is greater than30.

04

Part (b) Step 1: Explanation

The probability density function's symmetry and bell-shapedness determine how large sample size needed to be for a normal distribution to provide a good approximation to the distribution of x炉

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