High School

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 :

The correct answer is e) approximately normal with a mean 122 and standard deviation 0.35.

In this case, the distribution of the sample mean of IQ scores will be approximately normal because the sample size of 200 is sufficiently large. This is known as the Central Limit Theorem, which states that the distribution of the sample mean will be approximately normal as long as the sample size is large enough, regardless of the shape of the distribution of the population.

The mean of the sample mean distribution will be 122, which is the same as the mean of the population. The standard deviation of the sample mean distribution will be smaller than the standard deviation of the population because it is calculated using the sample size rather than the population size.

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