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.

The distribution of the sample mean of IQ scores is expected to be approximately normal with a mean of 122 and a standard deviation of 0.35, due to the Central Limit Theorem.

The distribution of the sample mean of IQ scores is expected to be approximately normal with a mean of 122 and a standard deviation of 0.35, due to the Central Limit Theorem. This theorem states that the sample means of any population will be approximately normally distributed, regardless of the population's original distribution, provided the sample size is sufficiently large. This is due to the fact that the sample means become increasingly less dependent on the individual scores and more dependent on the overall population distribution as the sample size increases. In this case, the population of adults has a mean IQ of 122 and a standard deviation of 5, and the sample size of 200 is large enough to produce a normal distribution for the sample mean. Therefore, the distribution of the sample mean of IQ scores is expected to be approximately normal with a mean of 122 and a standard deviation of 0.35.

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