Sampling students, continued. To estimate the mean score of those who took the M

Question

Sampling students, continued. To estimate the mean score of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.4. You want your sample mean to estimate with an error of no more than 1 point in either direction.
(a)
What standard deviation must have so that 99.7% of all samples give an within 1 point of ? (Use the 68–95–99.7 rule.)
(b)
How large an SRS do you need in order to reduce the standard deviation of to the value you found in part (a)?

Explanation / Answer

A) 99.7% of area covers mean + 3*sd.

So, 3*sd = 1

Or, standard deviation = 1/3 = 0.33

B) Standard error = 1/3

Or, 6.4/sqrt(n) = 1/3

Or, sqrt(n) = 6.4 * 3 = 19.2

Or, n = 369

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