A plan Is set before all state universities

A plan Is set before all state universities to require classmates to meet either three or four days a week in order to make better use of classroom facilities, because currently classrooms sit empty Friday afternoons and evenings and on Saturdays. However some schools that have a large percentage of commuter schools are concerned that this proposal will put a hardship on their computer students because it will require more driving to/from the campus. University officials want to estimate the average number of miles driven, one way, to campus by its commuter students. It is estimated that some students drive as little as 0 mile to campus while at least one student reported driving one way as far as 60 miles. University officials want to be 95% confident that the sample mean is no more than -+ 2 miles from the real average number of miles driven in the population.

a. What is the required sample size?

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b. After the study is conducted we learn that the standard deviation in the sample data, which is now our best estimate of s, is actually 12.3. What impact does this new measure of variation have on the mean number of miles driven that we also derived from our sample?