In a large population of college-educated adults, the mean IQ is 112 with standard deviation 25. Suppose 300 adults from this population are randomly selected for a market research campaign. The distribution of the sample mean IQ is: Group of answer choices

The sampling distribution of sample mean is N (112, 4.56).

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the sampling  distribution of the sample means will be approximately normally distributed.

Then, the mean of the sample means is given by,

And the standard deviation of the sample means is given by,

In this case, a sample of n = 30 college-educated adults were selected from a large population and their IQ levels were recorded.

The mean IQ level was, μ = 113.

The standard deviation of IQ was, σ = 25.

Since the sample size is large, i.e. n ≥ 30, then according to the Central limit theorem the sampling distribution of sample mean can be approximated by the Normal distribution.

The mean of the sampling distribution of sample mean is:

The standard deviation of the sampling distribution of sample mean is:

Thus, the sampling distribution of sample mean is N (112, 4.56).

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