The monthly demand for a certain magazine at a small shop, serving as a magazine agent, in Port of Spain has a Poisson distribution with mean 3.5. The shop always orders 4 copies of the magazine for sale each month; demand for the magazine that exceeds 4 is not met.

a. Find the probability that the shop will not be able to meet the demand in a given month.

b. A delivery service has a fleet of 60 trucks. At any time, the probability of a truck being out of use due to factors such as breakdowns and maintenance is 0.1.

i. What is the probability that 7 or more trucks are out of service?

ii. Use excel to compute the probability that 7 or more trucks are out of service, and compare this answer to part (i) above.

c. When the weather is extremely frigid, a motorist must charge his car battery during the night in order to improve the likelihood that the car will start early the following morning. If he does not charge it, the probability that the car will not start is 4/5. If he does charge it, the probability that the car will not start is 1/8. Past experience shows that the probability that he remembers to charge the battery is 9/10. One morning, during a cold spell, he cannot start his car. What is the probability that he forgot to charge the battery?