A random variable U is believed to be roughly normally distributed, and to have

Question

A random variable U is believed to be roughly normally distributed, and to have a standard deviation of 5.3 or less. The experimenters want to estimate the mean, with 95% confidence, to the nearest 0.5. That is, they want to choose a number of repetitions such that, for the average a from the experiment, they have 95% confidence that the true mean is between alpha - 0.5 and alpha + 0.5. Since experiments require money, time and effort, they wish to find a suitable n that is smallest necessary. Find n.

Explanation / Answer

here margin of error E =0.5

std deviation =5.3

for 95% CI, z=1.96

hence sample size =(z*std deviation/E)2  =~432

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