Long-haul trucks arrive at a vehicle equipment inspection station according to a Poisson process with rate ? = 24 trucks per hour. The probability that each arriving truck has no equipment violations is p = 0.85. Historically, it has been found that equipment violations are independent from one truck to another. a. What is the probability that exactly n trucks arrive in a random hour of operation? b. Plot the probability that exactly n trucks arrive in a random hour of operation (the function that you just identified). Plot the probability on the ordinate (vertical axis) versus n on the abscissa (horizontal axis) for n = 0, 1, . . . , 48. c. Given that exactly n trucks arrive in an hour, what is the probability that all n have no violations. d. What is the probability that exactly n trucks arrive in a random hour of operation AND that all n have no violations? e. What is the probability of finding no violations during a random hour of operation ?

Long-haul trucks arrive at a vehicle equipment inspection station according to a Poisson process with rate ? = 24 trucks per hour. The probability that each arriving truck has no equipment violations is p = 0.85. Historically, it has been found that equipment violations are independent from one truck to another. a. What is the probability that exactly n trucks arrive in a random hour of operation? b. Plot the probability that exactly n trucks arrive in a random hour of operation (the function that you just identified). Plot the probability on the ordinate (vertical axis) versus n on the abscissa (horizontal axis) for n = 0, 1, . . . , 48. c. Given that exactly n trucks arrive in an hour, what is the probability that all n have no violations. d. What is the probability that exactly n trucks arrive in a random hour of operation AND that all n have no violations? e. What is the probability of finding no violations during a random hour of operation ?