OBJECTIVES:

1.Correctly identify the probability distribution for each given problem.

2.Solve each problem using appropriate probability distribution function in Microsoft Excel.

3.Interpret the obtained result on each problem.

TASKS

Read and understand each item carefully. Identify the appropriate probability distribution and use Microsoft Excel as a tool to solve each problem.

1. A trading company uses six computers to trade on the Orlando Stock Exchange. The probability of a computer failing in a day is 0.321, and the computers fail independently. Computers are repaired in the evening, and each day is an independent trial. What is the probability that all six computers fail in a day?

2. Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the warning. Assume that a particular detection system has a 0.90 probability of detecting a missile attack.

a. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?

b. If three systems are installed, what is the probability that at least one of the systems will detect the attack?

c. Would you recommend that multiple detection systems be operated? Explain

3. The number of telephone calls that arrive at a phone exchange is often modelled as a Poisson random variable. Assume that on the average there are 7 calls per hour.

a.What is the probability that there are exactly 2 calls in one hour?

b.What is the probability that there are four or fewer calls in one hour?

c.What is the probability that there are exactly 26 calls in two hours?

4. Customers are known to arrive at La Buena Comida on a random basis with an average number of 24 customers per hour. What is the probability that 3 or less customers will arrive for a particular 10-minute interval?

5. Sick-leave time used by employees of a firm in one month approximates a normal distribution with a mean of 179 hours and a variance of 225. Find the probability that the total sick leave for next month will be less than 202.85 hours.

6. 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 = 28 days and s = 8 days.

a. What portion of the accounts is between 20 and 40 days old?

b. The hospital administrator is interested in sending reminder letters to the oldest 15% 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?

7.Sparagowski & Associates conducted a study of service times at the drive-up window of fast-food restaurants. The average time between placing an order and receiving the order at McDonald's restaurants was 2.78 minutes (The Cincinnati Enquirer, July 9, 2000). Waiting times, such as these, frequently follow an exponential distribution.

a. What is the probability that a customer's service time is less than 2 minutes?

b. What is the probability that a customer's service time is more than 5 minutes?

8. To boost holiday sales, a jewelry store in Bismarck, North Dakota, is advertising the following promotion: "If more than seven inches of cumulative snow fall on December 24, 25, 26, 27, and 28, you get your money back on all purchase made on December 17." To analyze this promotion, the store manager has collected data and determined that snowfall over this 5-day period in December is normally distributed with an average of 6 inches and standard deviation of 0.559 inches. What is the probability that the store will have to refund the money to its December 17 customers?