In a population of 210 women, the heights of the women are normally distributed with a mean of $64.9$ inches and a standard deviation of $3.2$ inches. If 49 women are selected at random, find the mean $\mu _ { \mathrm { X } } ^ { - }$and standard deviation $\sigma _ { \mathrm { x } } ^ { - }$of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor.

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Quizplus · Accepted Answer

The mean of the sample means $\mu _ { \mathrm { X } } ^ { - }$ is the same as the population mean, 64.9 inches. The standard deviation of the sample means $\sigma _ { \mathrm { x } } ^ { - }$ is calculated using the formula $\sigma / \sqrt{n} \times \sqrt{(N-n)/(N-1)}$, which gives approximately 0.4 inches.

In a Population of 210 Women, the Heights of the Women