please show all work

3) The systolic blood pressure (given in millimeters) of a group of 25 year olds has an approximately normal distribution with mean = 125 and standard deviation = 14. Systolic blood pressure for males follows a normal distribution.

a) Calculate the z-scores for the male systolic blood pressures 100 and 150 millimeters.

b) If a person is selected at random from this population, what is the probability that they have a blood pressure under 100 millimeters?

4) The switchboard in a Minneapolis law office gets an average of 5.5 incoming phone calls during the noon hour on Mondays. Experience shows that the existing staff can handle up to six calls in an hour. The distribution of calls at the law office can be described as a Poisson distribution where x = the number of calls received at noon.

a.) Find the mean and standard deviation of this Poisson distribution.

b) What is the probability that the office receives at most six calls at noon on Monday?

c) What is the probability that the office receives more than eight calls at noon?