Show your work in detail and write neatly and eligibly - KFUPM

KFUPM Term 081 Date: 20/12/2008

Mathematics & Statistics STAT 211 Duration: 15 minutes

Quiz# 3

Name: ID#: Serial#: Section#:

Show your work in detail and write neatly and eligibly
Q1. A company places a rush order for wire of two thicknesses. Consignments of

each thickness are to be sent immediately when they are available. Previous

experience suggests that the probability is 0.8 that at least one of these consignments

will arrive within a week. It is also estimated that, if the thinner wire arrives within

a week, the probability is 0.4 that the thicker wire will also arrive within a week.

Further, it is estimated that, if the thicker wire arrives within a week, the probability

is 0.6 that the thinner wire will also arrive within a week.

a. The probability that the thicker wire will arrive within a week =

b. The probability that the thinner wire will arrive within a week =

c. The probability that both consignments will arrive within a week =

Q2. The accompanying table shows, for 1,000 forecasts of earnings per share made

by financial analysts, the number of forecasts and outcomes in particular

categories (compared with the previous year).

Forecast

Outcome Improvement The same Worse

Improvement 210 82 66

The same 106 153 75

Worse 75 84 149

a. The probability that, if the forecast is for a worse performance
in earning, then the outcome is worse =

b. If the forecast is for an improvement in earnings, then the
probability that the outcome is an improvement =

With My Best Wishes

KFUPM Term 081 Date: 20/12/2008

Mathematics & Statistics STAT 211 Duration: 15 minutes

Quiz# 3

Name: ID#: Serial#: Section#:

Show your work in detail and write neatly and eligibly
Q1. In a large city, 8% of the inhabitants have contracted a particular disease. A test

for this disease is positive in 80% of people who have the disease and is

negative in 80% in the people who do not have the disease. Then,

The probability that a person for whom the test result is positive
has the disease =

Q2. A contractor estimates the probabilities for the number of days required to

complete a certain type of construction project as follows:

Time (days) 1 2 3 4 5
Probability 0.05 0.20 0.35 0.30 0.10

a. The probability that a randomly chosen project will take less than 3
days to complete =

b. The expected time required to complete a project =

c. The contractor’s project is made up of two parts–a fixed cost of
$20,000, plus $2,000 for each day taken to complete the project. The
mean of the total cost of the project =

d. If three projects are undertaken, and assuming independence of
individual project completion times, then the probability that at
most two of them will take at least 4 days to complete =

With My Best Wishes

KFUPM Term 081 Date: 20/12/2008

Mathematics & Statistics STAT 211 Duration: 15 minutes

Quiz# 3

Name: ID#: Serial#: Section#:

Show your work in detail and write neatly and eligibly
Q1. A restaurant manager classifies customers as well dressed, moderately

dressed, or poorly dressed and finds that of all customers 50%, 40%, and 10%

respectively, fall into these categories. The manager found that soda was

ordered by 50% of the well-dressed customers, by 70% of the moderately

dressed, and by 30% of the poorly dressed.

a. The probability that a randomly chosen customer orders soda =

b. If a soda is ordered, then the probability that the person is ordering
is well dressed =

c. If soda is ordered, then the probability that the person ordering is
not well dressed =

Q2. Using detailed cash flow information, a financial analyst claims to be able to

spot companies that are likely candidates for bankruptcy. The analyst is
presented with information on the past records of 15 companies and told that,
in fact, 4 of these have failed. He selects, as candidates for failure, 5 companies
from the group of 15.
a. The probability that he will find 2 failed companies =

b. The probability that he will find at least 4 failed companies =

With My Best Wishes