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.

Expert verified

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

Step by step solution

The mean is $μ = 122$

Standard deviation is $σ = 5$

The number of persons $n = 200$

The following concept was used:

$σ_{\bar{x}} = \frac{σ}{\sqrt{n}}$

The sample size is larger than 33.

By Know that the sampling distribution of the central limit theorem sample mean $\bar{x}$ is concerned with the ordinary.

$μ \bar{x} = μ = 122 σ_{\bar{x}} = \frac{σ}{\sqrt{n}} = \frac{5}{\sqrt{200}} = 0 .35$

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.

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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