91Ó°ÊÓ

The distribution of IQ scores is strongly left-skewed with a mean of $122$and a standard deviation of $5$.

$200$ adults are randomly selected and the IQ score is found.

The population is strongly left-skewed

$\mathrm{μ}=Mean=122$$\mathrm{σ}=S\tan darddeviation=5$

$n=Samplesize=200$

If the sample is large enough, the central limit theorem states that the sampling distribution of the sample mean is approximately normal. When a sample size of$30$or more is used, it is regarded as adequately large.

The sample size $200$in this situation is an adequate sample size.

We know that the sampling distribution of the sample mean $\overline{x}$is approximately normal because of the central limit theorem.

${\mathrm{μ}}_{\stackrel{¯}{x}}=\mathrm{μ}=122$

The population standard deviation divided by the square root of the sample size yields the standard deviation of the sampling distribution of the sample mean $\overline{x}$

${\mathrm{σ}}_{\stackrel{¯}{x}}=\frac{\mathrm{σ}}{\sqrt{n}}=\frac{5}{\sqrt{200}}≈0.35$

Thus it is approximately normal with a mean$122$and standard deviation$0.35.$