To estimate the mean score mu of those who took the Medical College Admission Te

Question

To estimate the mean score mu 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 6.3. You want your sample mean x to estimate mu with an error of no more than 1.3 point in either direction. (a) What standard deviation (plusminus 0.0001) must x have so that 99.7% of all samples give an x within 1.3 point of mu? (b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found in part (a)?

Explanation / Answer

here as we know that standard deviation =margin of error/z score

for z score for 99.7% =2.9677

hence std deviation of mean =1.3/2.9677=0.438044

b) fpr sample size=(std deviation of [population/std deviation of mean)2 =(6.3/0.438044)2=~207

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