Write a program (using MINITAB or other software) to generate 100 random samples of size 100 from a population that has a standard normal distribution. Then use the 100 samples to construct one hundred 90% tolerance intervals to contain at least 95% of the population.
(a) Did any of the intervals contain exactly 95% of the population?
(b) If not, should we say, generally, that a tolerance interval designed to contain at least 95% of the population will actually contain more than 95% in the same way that P (X ≥ 1.96) = P (X > 1.96) when X has a standard normal distribution? Explain.