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Statistics / The Practice of Statistics 5 / Chapter 7 / Problem AP2.3

The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor

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Section I: Multiple Choice Choose the best answer for each question. In a certain large

Chapter 7, Problem AP2.3

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QUESTION:

Section I: Multiple Choice Choose the best answer for each question. 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. The distribution of the sample mean of IQ scores 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.

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QUESTION:

Section I: Multiple Choice Choose the best answer for each question. 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. The distribution of the sample mean of IQ scores 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.

ANSWER:

Step 1 of 2

Given: Population is strongly left-skewed

The central limit theorem tells us that the sampling distribution of the sample mean is approximately normal, if the sample is sufficiently large. A sample is considered to be sufficiently large when the sample size is 30 or more.

In this case, the sample size is 200 and thus the sample is sufficiently large. By the central limit theorem, we then know that the sampling distribution of the sample mean is approximately normal.

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