1. A particular production process produces bolts whose diameter is a N ( 3, 16) random variable.
(a) Find the probability that a randomly selected bolt will have a diameter less than 3.2.
(b) Find the probability that the average diameter from a sample of 35 bolts will be less than 3.2.
2. Customers arrive at a counter in accordance with a Poisson process of density three arrivals per minute.
(a) What is the expected number of arrivals per minute?
(b) What is the standard deviation of the number of arrivals per minute?
(c) Use the CLT to approximate the probability that the average number of arrivals in 75 I-minute periods is between 2.6 and 3.4.