Managerial Statistics 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
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
b) How many experimental runs are there that involve use of the
lowest temperature and two lowest pressures along with the five
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?
Managerial Statistics 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?
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?
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)?
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?
Managerial Statistics 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?
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)
Problems with electricity supplied
Malfunctioning electrical equipment
Caused by other human errors
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.