A random sample of 16 students in the School of Economics and Finance was taken to estimate average daily commuting time for all the students. Suppose that the population times have a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes.

a) Find the probability that the average daily commuting time is fewer than 100 minutes. Also, find the probability that it is outside the range of 85 to 95 minutes.

b) Suppose that a second independent random sample of 50 students is taken. Without doing the calculations, explain whether the probabilities in part (a) would be higher, lower, or the same for the second sample. Justify your answer