Question

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 6.2 . You want your sample mean ?¯ to estimate ? with an error of no more than 0.8 point in either direction.

(a) What standard deviation must ?¯ have so that 99.7% of all samples give an ?¯ within 0.8 point of ?μ? Use the 68–95–99.7 rule. (Enter your answer rounded to four decimal places.)

standard deviation of ?¯=

(b) How large an SRS do you need in order to reduce the standard deviation of ?¯to the value you found? (Enter your answer rounded to the nearest whole number.)

SRS size =

Answer 1

a) According to empirical rule, 99.7% of the observations lies within 3 standard deviations of the mean.

therefore we have here:

Therefore 0.2667 is the required standard deviation here.

b) The standard deviation for population is given to be 6.2 here. Therefore, we have here:

Therefore, the sample size here is computed as:

Therefore 541 is the required sample size here.