In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. The distribution of the sample mean IQ is?

Solution:

It is given that the mean IQ is 112 with a standard deviation of 20.

Let us assume X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

x ~ N

Where, μ = 112, σ = 20

Since the distribution for X is normal then the distribution for the sample mean x̄ is also normal and given by:

X̄  ~ N(μ, σ/√n)

μX̄ = 112

σX̄ = 20/√200

σX̄ = 1.414

Therefore, the distribution of the sample mean IQ is 1.414

In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. The distribution of the sample mean IQ is?

Summary:

In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. The distribution of the sample mean IQ is 1.414