A woman working in telemarketing makes telephone calls to private homes according to a Poisson process with rate λ = 100 per (working) day. We estimate that the probability that she succeeds in selling her product, on a given call, is equal to 5%, independently from one call to another. Let N(t) be the number of telephone calls made in the interval [0, t], where t is in (working) days, and let X be the number of sales made during one day.

(a) Suppose that the woman starts her working day at 9 a.m. and stops working at 7 p.m. Let TQ be the number of minutes between 9 a.m. and the moment of her first call of the day, and let SQ be the duration (in minutes) of this call. We suppose that SQ ~ Exp(l) and that TQ and 5o are independent random variables. What is the probability that the woman has made and finished her first call at no later than 9:06 a.m. on an arbitrary working day?

(d) What is the probability that the woman will make no sales at all on exactly one day in the course of a week consisting of five working days?