A simple random sample of size 10 drawn from a normal distribution yielded a sample mean of 100 and a sample variance of 64.

i) Obtain a 99% confidence interval for the true mean of the population

ii) What would the interval be if the population variance were known to be

σ^2 = 81?

iii) If it is required to be 95% confident that the sample mean is to be correct to within 2 euro of the true mean ,what samle size is necessary? Use σ^2 = 81.