A random sample of sixteen junior managers in the offices of corporations in a large city. center was taken in order to estimate average daily commuting times for all such man- agers. Suppose that the population times have a normal distribution with mean 87 minutes and standard deviation 22 minutes.

(a) What is the standard error of the sample mean commuting time?

(b) What is the probability that the sample mean is less than 100 minutes?

(c) What is the probability that the sample mean is more than 80 minutes?

(d) What is the probability that the sample mean is outside the range 85 to 95 minutes?

(e) Suppose that a second (independent) random sample, of fifty junior managers, is taken. Without doing the calculations, state whether the probabilities in parts (b), (c). and

(d) would be higher, lower, or the same for the second sample. Sketch graphs to illustrate your answers.