1. The French bread made at La Fleur de Farine costs $8 per dozen baguettes to produce. Fresh bread sells at a premium, $16 per dozen baguettes, but it has a short shelf life. If La Fleur de Farine bakes more bread than its customers demand on any given day, the leftover day-old bread goes for croutons in local restaurants at a discounted $7 per dozen baguettes. Conversely, producing less bread than customers demand leads to lost sales. La Fleur de Farine bakes its French bread in batches of 350 dozen baguettes. The daily demand for bread is a random variable, taking the values two, three, four, or fi ve batches, with probabilities 0.2, 0.25, 0.4, and 0.15, respectively. If La Fleur de

Reginald Dunfey, president of British World Airlines, is fiercely proud of his company's on time percentage; only 2 percent of all BWA flights arrive more than 10 minutes early or late. In his upcoming speech to the BWA board of directors, Mr. Dunfey wants to include the probability that none of the 200 flights scheduled for the following week will be more than 10 minutes early or late. What is the probability? What is the probability that exactly 10 flights will be more than 10 minutes early or late?

The City Bank of Durham has recently begun a new credit program. Customers meeting

certain credit requirements can obtain a credit card accepted by participating area merchants

that carries a discount. Past numbers show that 25 percent of all applicants for this card are

rejected. Given that credit acceptance or rejection is a Bernoulli process, out of 15 applicants,

what is the probability that

(a) Exactly four will be rejected?

(b) Exactly eight?

(c) Fewer than three?

(d) More than fi ve?

latest styles. Therefore, the company's weekly orders of wool cloth are diffi cult to predict in

advance. On the basis of 5 years of data, the following probability distribution for the company's

weekly demand for wool has been computed:

Amount of wool (lb) 2,500 3,500 4,500 5,500

Probability 0.30 0.45 0.20 0.05

From these data, the raw-materials purchaser computed the expected number of pounds

required. Recently, she noticed that the company's sales were lower in the last year than in

years before. Extrapolating, she observed that the company will be lucky if its weekly demand

averages 2,500 this year.

(a) What was the expected weekly demand for wool based on the distribution from past data?

(b) If each pound of wool generates $5 in revenue and costs $4 to purchase, ship, and handle,

how much would Giles Fashion stand to gain or lose each week if it orders wool

based on the past expected value and the company's demand is only 2,500?

Heidi Tanner is the manager of an exclusive shop that sells women's leather clothing and

accessories. At the beginning of the fall/winter season, Ms. Tanner must decide how many

full-length leather coats to order. These coats cost her $100 each and will sell for $200 each.

Any coats left over at the end of the season will have to be sold at a 20 percent discount in

order to make room for spring/summer inventory. From past experience, Heidi knows that

demand for the coats has the following probability distribution:

Number of coats demanded 8 10 12 14 16

Probability 0.10 0.20 0.25 0.30 0.15

She also knows that any leftover coats can be sold at discount.

(a) If Heidi decides to order 14 coats, what is her expected profi t?

(b) How would the answer to part (a) change if the leftover coats were sold at a 40 percent

discount?

The Executive Camera Company provides full expenses for its sales force. When attempting

to budget automobile expenses for its employees, the fi nancial department uses mileage fi gures

to estimate gas, tire, and repair expenses. Distances driven average 5,650 miles a month,

and have a standard deviation of 120. The fi nancial department wants its expense estimate and

subsequent budget to be adequately high and, therefore, does not want to use any of the data

from drivers who drove fewer than 5,500 miles. What percentage of Executive's sales force

drove 5,500 miles or more?

Mission Bank is considering changing the day for scheduled maintenance for the automatic

teller machine (ATM) in the lobby. The average number of people using it between 8 and

A.M. is 30, except on Fridays, when the average is 45. The management decision must balance

the effi cient use of maintenance staff while minimizing customer inconvenience.

a) Does knowledge of the two average fi gures affect the manager's expected value (for

inconvenienced customers)?

b) Taking the data for all days together, the relative probability of inconveniencing 45 customers

is quite small. Should the manager expect many inconvenienced customers if the

maintenance day is changed to Friday?

The purchasing agent in charge of procuring automobiles for the state of Minnesota's interagency

motor pool was considering two different models. Both were 4-door, 4-cylinder cars

with comparable service warranties. The decision was to choose the automobile that achieved

the best mileage per gallon. The state had done some tests of its own, which produced the following

results for the two automobiles in question:

Average MPG Standard Deviation

Automobile A 42 4

Automobile B 38 7

The purchasing agent was uncomfortable with the standard deviations, so she set her own

decision criterion for the car that would be more likely to get more than 45 miles per gallon.

a) Using the data provided in combination with the purchasing agent's decision criterion,

which car should she choose?

b) If the purchasing agent's criterion was to reject the automobile that more likely obtained

less than 39 mpg, which car should she buy?

Ted Hughes, the mayor of Chapelboro, wants to do something to reduce the number of accidents

in the town involving motorists and bicyclists. Currently, the probability distribution

the number of such accidents per week is as follows:

Number of accidents 0 1 2 3 4 5

Probability 0.05 0.10 0.20 0.40 0.15 0.10

The mayor has two choices of action: He can install additional lighting on the town's streets

or he can expand the number of bike lanes in the town. The respective revised probability

distributions for the two options are as follows:

Number of accidents 0 1 2 3 4 5

Probability (lights) 0.10 0.20 0.30 0.25 0.10 0.05

Probability (lanes) 0.20 0.20 0.20 0.30 0.05 0.05

Which plan should the mayor approve if he wants to produce the largest possible reduction

(a) Expected number of accidents per week?

(b) Probability of more than three accidents per week?

(c) Probability of three or more accidents per week?

Copy Chums of Boulder leases offi ce copying machines and resells returned machines

discount. Leases are normally distributed, with a mean of 24 months and a standard deviation

of 7.5 months.

(a) What is the probability that a copier will still be on lease after 28 months?

(b) What is the probability that a copier will be returned within one year?

D'Addario Rose Co. is planning rose production for Valentine's Day. Each rose costs $0.35 to

raise and sells wholesale for $0.70. Any roses left over after Valentine's Day can be sold the

next day for $0.10 wholesale. D'Addario has the following probability distribution based on

previous years:

Roses sold 15,000 20,000 25,000 30,000

Probability 0.10 0.30 0.40 0.20

How many roses should D'Addario produce to minimize the fi rm's expected losses?

Ansel Fearrington wants to borrow $75,000 from his bank for a new tractor for his farm. The

loan offi cer doesn't have any data specifi cally on the bank's history of equipment loans, but

he does tell Ansel that over the years, the bank has received about 1460 loan applications per

year and that the probability of approval was, on average, about 0.8.

a) Ansel is curious about the average and standard deviation of the number of loans

approved per year. Find these fi gures for him.

b) Suppose that after careful research the loan offi cer tells Ansel the correct fi gures actually

are 1,327 applications per year with an approval probability of 0.77. What are the mean

and standard deviation now?