Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour.

(a) Determine the mean and standard deviation of the number of cabs per 10-hour day.

(b) Approximate the probability that more than 65 cabs pass within a 10-hour day.

(c) Approximate the probability that between 50 and 65 cabs pass in a 10-hour day.

(d) Determine the mean hourly rate so that the probability is approximately 0.95 that 100 or more cabs pass in a 10-hour data.