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Managerial Statistics I

1.

Exam I

Solve the following problems:

I. A computer rating service is commissioned to rank 10 different brands of flat

screen LCD monitors. The rating service is to rank the top three brands in

order, 1 through 3 (12 points)

a) In how many different ways can the computer rating service arrive

at the final ranking?

b) If the rating service can distinguish no difference among the

brands, and therefore arrives at the final ranking by chance, what

is the probability that one particular brand (call it Company Z’s

brand) is ranked first?

c) Suppose that the computer rating service is to choose the top

three from the group of 10, but is not to rank the three? In how

many different ways can the rating service choose the three to be

designated “top of the line” flat screen LCD monitors

d) Consider the same information as part c and assume the rating

service makes its choice by chance. Say there is a company

(company X) that has two brands in the group of 10. What is the

probability that one of company’s X brands is selected in the top

three?

II. An experimenter is studying the effects of temperature, pressure and type of

catalyst on yield from a certain chemical reaction. Three different

temperature, four different pressures and five different catalysts are under

consideration: (12 points)

a) If any particular experimental run involves the use of a single

temperature, pressure and catalyst, how many experimental runs

are possible?

b) How many experimental runs are there that involve use of the

lowest temperature and two lowest pressures along with the five

catalyst?

c) Suppose that five different experimental runs are to be made on

the first day of experimentation. If the five are randomly selected

from among all the possibilities, so that any group of five has the

same probability of selection, what is the probability that a

different catalyst is used on each run?

ENMGT 571

Managerial Statistics I

III.

Exam I

A mathematics professor wishes to schedule an appointment with each of

her eight teaching assistants, four men and four women, to discuss her

calculus course. Suppose all possible orderings of appointments are equally

likely to be selected. (15 points)

a) What is the probability that at least one female assistant is among

the first three of whom the professor meets?

b) What is the probability that after the first five appointments, she has

met with all female assistants?

IV.

A real estate agent has 8 master keys to open several new homes. Only 1

master key will open any given house. If 40% of these homes are usually

left unlocked, (10 Points)

a) what is the probability that the real estate agent can get into a

specific home if the agent selects 3 master keys at random before

leaving the office?

V.

The US Army Corps of Engineers’ study on the DDT contamination of fish

in the Tennessee River (Alabama) revealed the following: 52 percent of the

fish are found between 275 and 300 miles, 39% are found between 305 and

325 miles and 9% are found between 330 and 350 miles (10 points)

a) Given that a contaminated fish is found in a certain distance

upstream, the probability that it is a channel catfish (CC) is

determined from the data as P(CC/275-300)=.775,

P(CC/305-325) = .77 and P(CC/330-350) =.86. If a contaminated

catfish is captured from the Tennessee River, what is the

probability that it was captured 275-300 miles upstream?

b) What is the probability of being a channel catfish (CC)?

2.

A box in a certain supply room contains eleven 40-W light bulbs and nine 75-W

bulbs. Suppose that three bulbs are randomly selected(15 pts)

a. What is the probability that exactly two of the of the selected bulbs are rated 75W?

b. What is the probability that at least one 40W bulb is selected?

c. Given a 40-W bulb is selected on the first draw, what is the probability of

selecting exactly one more 40-W?

ENMGT 571

Managerial Statistics I

3.

Exam I

A market study taken at a local sporting goods store showed that of 30 people

questioned, 18 owned tents, 15 owned sleeping bags, 14 owned camping stoves,

6 owned both tents and camping stoves, and 10 owned both sleeping bags and

camping stoves: (15 pts)

a. What is the probability of owning a tent, owning a camping stove, owning

a sleeping bag, owning both a tent and a camping stove, and owning both

a sleeping bag and a camping stove?

b. What is the probability of owning a tent or a camping stove?

c. What is the probability of owning neither a camping stove or a tent

d. Given a person questioned owns a tent, what is the probability he also

owns a camping stove?

e. Are the events of owning a tent and owning a camping stove mutually

exclusive? Explain briefly?

f. Are the events of owning a sleeping bag and owning a camping stove

independent? Explain Briefly?

g. If four people questioned owned a tent, a sleeping bag, and a camping

stove, then up to how many can own only a camping stove?

4.

A regional telephone company operates three identical relay stations at

different locations. During a one-year period, the number of malfunctions

reported by each station and the causes are shown below. (11 pts)

______Stations:

Problems with electricity supplied

Computer malfunction

Malfunctioning electrical equipment

Caused by other human errors

A

6

4

5

7

B

1

4

4

9

C___

1

2

1

5

a. What is the probability of a Computer Malfunction?

b. What is the probability that station A will experience malfunction

with electrical equipment?

c. Suppose (given) that a malfunction was reported and it was

found to be caused by other human errors. What is the

probability that it came from station C?

d. Given we have a problem at station B, What is the probability

that it is a problem other than a computer malfunction?

Level of Detail: Show all work

Other Requirements: Please answer questions and show all work for 1 (I, II, III, IV, V) and 2 (a, b, c). I already have completed 3 and 4.

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