Suppose that wait times for customers at a grocery store cashier line are uniformly distributed between one minutes and fifteen minutes. (a) What are the mean and variance of the waiting time? (b) What is the probability that a customer waits less than seven minutes? (c) What is the probability that a customer waits between four and twenty minutes? (d) Suppose that a customer who waits k minutes in line receives a coupon worth a 0.2 k 1/4 dollar discount on a future visit. What is the mean of the coupon value for a customer?
Suppose that the weights of cinder blocks at a local construction yard follow a normal distribution with mean of 20 kg and a variance of 0.25 kg2. (a) What is the probability that a cinder block weighs at most 20.6 kg? (b) What is the probability that a cinder block weighs more than 19.8 kg? (c) What is the probability that a cinder block weighs between 19.9 and 20.2 kg? (d) Find the weight, wU, that will be exceeded by 5% of cinder blocks. (e) Find the weight, wL, that will be exceeded by 99% of cinder blocks.