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MCQs: Probability

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1. A company has 3 goals, listed in order of importance.
1. Achieve a total profit of at least $240 million.
2. Maintain the current employment level of 3,000 employees.
3. Invest no more than $70 million in capital.
What is the objective function for a goal program for this situation?

A) P1d1-, P2d2-, P3d3+
B) P1d1-, P2d2+, P2d2-, P3d3-
C) P1d1-, P2d2-, P2d2-, P3d3+
D) P1d1+, P2d2-, P2d2-, P3d3+

2. A customer molder produces 6-ounce juice glasses and 10-ounce cocktail glasses. The per unit contribution for the juice glasses (x1) is equal to 60-5x1, and the per unit contribution for the cocktail glasses (x2) is 80-4x2. An expression for the total contribution is:

A) 20 - 4x2 - 5x1
B) 60x1 - 5x1^2 + 80 x2 - 4x2^2
C) 80x1 - 5x1^2 + 60x2 - 4x2^2
D) 20 - (4x2)(5x1)

3, 4 and 5

Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y.

3) What is the probability that Jim will be accepted at both universities?
4) What is the probability that Jim will not be accepted at either universities?

5) A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is more than 24 oz?

6) The University Sweepstakes has the following payoffs and probabilities. Each person is limited one entry.

Please see the attachment for the probability distribution.

The probability that someone wins any money is------------

7) An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week?

A) 2.12
B) 3.32
C) 4.12
D) 2.83

8) The professor would like to assign grades such that 5% of students receive As. If the exam average is 62 with a standard deviation of 13, what grades should be the cutoff for an A? (Round your answer)

A) 80
B) 83
C) 90
D) 93

9) Given the following data on the number of pints of ice cream sold at a local ice cream store for a 6-period time frame:

Period Demand

1 200
2 245
3 190
4 270
5 280
6 300

Compute a 3-period moving average for period 4.
Please see the attached questions.

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The solution provides answers to multiple choice questions on probability and moving average. Relevant workings are also included.

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Independent Events

27. In 1998, the average age of students at UTC was 22 with a standard deviation of 3.96.
In 1999, the average age was 24 with a standard deviation of 4.08. In which year do
the ages show a more dispersed distribution? Show your complete work.

29. If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then
P(A  B) =
a. 0.76
b. 1
c. 0.24
d. 0.2
e. None of the above answers is correct.

30. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9.
One chip is selected at random from each urn. The total number of sample
points in the sample space is _____
a. 30
b. 100
c. 729
d. 1,000
e. None of the above answers is correct.

31. A six-sided die is tossed 3 times. The probability of observing three ones in a row is

a. 1/3
b. 1/6
c. 1/27
d. 1/216
e. None of the above answers is correct.

32. If P(A) = 0.38, P(B) = 0.83, and P(A  B) = 0.57; then P(A  B) =
a. 1.21
b. 0.64
c. 0.78
d. 1.78
e. None of the above answers is correct.
Use this data to answer questions 34 and 35.
A sample of 2,500 people was asked how many cups of coffee they drink in the morning.
You are given the following sample information.
Cups of Coffee Frequency
0 700
1 900
2 600
3 300
2,500

34. The expected number of cups of coffee is
a. 1
b. 1.2
c. 1.5
d. 1.7
e. None of the above answers is correct.

35. The variance of the number of cups of coffee is
a. 0.96
b. 0.9798
c. 1
d. 2.4
e. None of the above answers is correct.

Please use the information in this paragraph to answer questions 36 - 40.
The random variable x is the number of occurrences of an event over an interval of ten
minutes. It can be assumed that the probability of an occurrence is the same in any two
time periods of an equal length. It is known that the that the probability of an occurrence
is the same in any two time periods of an equal length. It is known that the mean number
of occurences in ten minutes is 5.3.

36. The random variable x satisfies which of the following probability distributions?
a. normal
b. Poisson
c. binomial
d. Not enough information is given to answer this question.
e. None of the above answers is correct.

37. The appropriate probability distribution for the random variable is
a. discrete
b. continuous
c. either a or b depending on how the interval is defined
d. not enough information is given
e. None of the above answers is correct.

38. The expected value of the random variable x is
a. 2
b. 5.3
c. 10
d. 2.3
e. None of the above answers is correct.

39. The probability that there are 8 occurrences in ten minutes is
a. 0.0241
b. 0.0771
c. 0.1126
d. 0.9107
e. None of the above answers is correct.

40. The probability that there are less than 3 occurrences is
a. 0.0659
b. 0.0948
c. 0.1016
d. 0.1239
e. None of the above answers is correct.

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