1)General Hospital's patient account division has compiled data on the age of accounts receivable. The data collected indicate that the age of the accounts follows a normal distribution with =2 months (60 days) and =8 days.

a. What portion of the accounts is between 40 and 55 days oldthat is, P (40 x 55)?

b. The hospital administrator is interested in sending reminder letters to the oldest 25% of accounts. How many days old should an account be before a reminder letter is sent?

c. The hospital administrator wants to give a discount to those accounts that pay their balance by the twenty-first day. What percentage of the accounts will receive the discount?

2)The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.

a. Sketch this exponential probability distribution.

b. What is the probability that the time between vehicle arrivals is 12 seconds or less?

c. What is the probability that the time between vehicle arrivals is 6 seconds or less?

d. What is the probability that there will be 30 or more seconds between arriving vehicles?

3)A coffee machine dispenses coffee uniformly between 200 and 240 ml of coffee each time it is used.

a)What is the chance that a customer's coffee is between 220 and 230 ml in volume?

b)What is the chance a customer receives a coffee cup from this machine with less than 180 ml of coffee?