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Chapter 7: Q. 2.3 (page 488)

In a certain large population of adults, the distribution of IQ scores is strongly left skewed with a mean of 122 and a standard deviation of 5. Suppose 200 adults are randomly selected from this population for a market research study. For SRSs of size 200, the distribution of sample mean IQ score is

a. left-skewed with mean 122 and standard deviation 0.35.

b. exactly Normal with mean 122 and standard deviation 5.

c. exactly Normal with mean 122 and standard deviation 0.35.

d. approximately Normal with mean 122 and standard deviation 5.

e. approximately Normal with mean 122 and standard deviation 0.35.

Short Answer

Expert verified

(e) Approximately normal with mean is 122 and standard deviation is 0.35

Step by step solution

01

Given Information 

The mean is 渭=122

Standard deviation is 蟽=5

The number of persons n=200

The following concept was used:

蟽x炉=蟽n

02

Explanation for correct option 

The sample size is larger than 33.

By Know that the sampling distribution of the central limit theorem sample meanx炉is concerned with the ordinary.

渭x炉=渭=122蟽x炉=蟽n=5200=0.35

As a result, the sample mean's sampling distribution is close to normal, with a mean of 122 and a standard deviation of 0.35.

03

Explanation for incorrect option 

a. left-skewed with not provided mean 122 and standard deviation 0.35

b. exactly Normal with not provided mean 122 and standard deviation 5

c. exactly Normal with not provided mean 122 and standard deviation 0.35

d. approximately Normal with not provide mean 122 and standard deviation 5

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