6.39 The breakdowns of an industrial robot follow a Poisson distribution with an average of C = 100 + 40X + 3X 2

0.5 breakdowns per 8-hour workday. The robot is placed in service at the beginning of the day.

a Find the probability that it will not breakdown during the day.

b Find the probability that it will work for at least 4 hours without breaking down.

c Does what happened the day before have any effect on your answers above? Why?