to estimate the mean score of those who took the medical college admission test

Question

to estimate the mean score of those who took the medical college admission test on your campus, you will obtain the scores of a random sampe of students. from published information, you know that the scores are approximately normal with standard deviation about 6.5. you want your sample mean to estimate the mean score with an error of no more than 1 point in either direction. What standard deviation must sample mean have so that 99.7 percent of all samples give a sample mean within 1 point of mean score (margin of error) using the 68-95-99.7 rule

Explanation / Answer

Let standard deviation of sample mean be x. By rule, 99.7% of observations lie between 3 standard deviations from the mean. Hence,

3*s = 1

s = 1/3

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