1) Suppose a random variable, x, has a uniform distribution with a=4 and b=12.

a. Calculate P(4.5x11).

b. Determine P(x>8).

c. Compute the mean, , and the standard deviation, , of this random variable.

d. Determine the probability that x is in the interval (3).

2) The useful life of an electrical component is exponentially distributed with a mean of 2,000 hours

a. What is the probability the circuit will last more than 2,250 hours?

b. What is the probability the circuit will last between 2,000 and 2,500 hours?

c. What is the probability the circuit will fail within the first 1,500 hours?

3) The time required to prepare a certain specialty coffee at a local coffee shop is uniformly distributed between 30 and 40 seconds. Assuming a customer just ordered one of these specialty coffees, determine the probabilities described below.

a. What is the probability that the preparation time will be more than 33 seconds?

b. What is the probability that the preparation time will be between 34 and 37 seconds?

c. What percentage of these specialty coffees will be prepared within 35 seconds?

d. What is the standard deviation of preparation times for this specialty coffee at this shop?

4)A delicatessen is open 24 hours a day every day of the week. On the average, 24 orders are received by fax every two hours throughout the day.

a. Find the probability that a faxed order will arrive within the next 6 minutes.

b. Find the probability that the time between two faxed orders will be between 2 and 3 minutes.

c. Find the probability that 15 or more minutes will elapse between faxed orders.