91影视

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

$渭=Mean=122$$蟽=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.

${渭}_{\stackrel{炉}{x}}=渭=122$

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 $\overline{x}$

${蟽}_{\stackrel{炉}{x}}=\frac{蟽}{\sqrt{n}}=\frac{5}{\sqrt{200}}鈮�0.35$

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