Cars arrive at an inspection station according to a Poisson distribution at a rate of 10 cars per hour (λ = 10). With probability of 0.5, a car will pass inspection. a. What is the expected number of cars to arrive at the inspection station in 1 hour? What is the expected number of cars to arrive in a 3 hour period? b. What is the probability that at most (less than or equal to) 15 cars will arrive in the 1 hour time period? Write out the theoretical form and use R to compute a numeric value.

Let X denote the waiting time (in minutes) for a customer. An assistant manager claims that μ, the average waiting time of the entire population of customers, is 2 minutes with standard deviation also 2 minutes. The manager doesn't believe his assistant's claim, so he observes a random sample of 36 custoers. The average waiting time for the 36 customers is 3.2 minutes. What is the probability that the average of 36 customers is 3.2 minutes or more? Do you think that assistant manager's claim that the mean is 2 minutes is correct?

20)

6. The life expectancy of a brand of car motors has a normal distribution with "- 75,000 and o - 5,500. a. Find the probability that 1 motor is chosen at random will have a life expectancy of more than 90,000 miles.