Q$1.$ The amount of time a law counselor spends with each client follows a normal distribution with

a population mean of $35$ minutes and a standard deviation of $11$ minutes.

a$.$ If a random sample of $16$ and $25$ clients is selected respectively, what is the probability that

the average time spent per client will be at least $37$ minutes?

b$.$ Explain why two probability values differ in Part a by drawing a graph to illustrate your

reasoning. Compare variability and dispersion of the curves for each sample size.

c$.$ If a random sample of $25$ clients is selected there is a $35\%$ chance that the sample mean

will be below how many minutes?