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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.