In a population of 225 women, the heights of the women are normally distributed with a mean of 64.5 inches and a standard deviation of 2.9 inches. If 25 women are selected at random, find the probability that their mean height will exceed 66 inches. Assume that the sampling is done without replacement and use a finite population correction factor with $\mathrm { N } = 225$

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Quizplus · Accepted Answer

The probability is calculated using the finite population correction factor and the standard error of the mean. The corrected standard error is smaller due to the finite population, and using the z-score formula, the probability of the sample mean exceeding 66 inches is found to be approximately 0.0031.

In a Population of 225 Women, the Heights of the Women