Question

To estimate the mean score μμ 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 6.6. You want your sample mean x⎯⎯⎯x¯ to estimate μμ with an error of no more than 1 point in either direction.

(a) What standard deviation (±±0.0001) must x⎯⎯⎯x¯ have so that 99.7% of all samples give an x⎯⎯⎯x¯ within 1 point of μμ?

(b) How large an SRS do you need in order to reduce the standard deviation of x⎯⎯⎯x¯ to the value you found in part (a)?

Answer 1

In statistics, we have the 68–95–99.7 rule, also known as the three-sigma rule or empirical rule, states that nearly all values lie within three standard deviations of the mean in a normal distribution. This rule we can apply here to find the solution.

We have to find SD , such that

By the question   must be equal to 1 for all samples, so,

Standard Deviation must have 0.333,

So that 99.7% of all samples give an within 1 point of μ.