”
Chapter 11 7. The following probabilities for grades in management science have been determined based on past
records:
Grade Probability
A 0.1
B 0.2
C 0.4
D 0.2
F 0.10
1.00
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the
expected grade and variance for the course. 8. An investment firm is considering two alternative investments, A and B, under two possible future
sets of economic conditions good and poor. There is a .60 probability of good economic conditions
occurring and a .40 probability of poor economic conditions occurring. The expected gains and
losses under each economic type of conditions are shown in the following table:
Investment
Economic Conditions
Good Poor
A $380,000 -$100,000
B $130,000 $85,000
Using the expected value of each investment alternative, determine which should be selected. 9. The weight of the bags of fertilizer is normally distributed, with a mean of 45 pounds and a
standard deviation of 5 pounds. What is the probability that a bag of fertilizer will weigh between
38 and 50 pounds?
MAT540 Homework
Week 1
Page 3 of 3 10. The polo Development Firm is building a shopping center. It has informed renters that their rental
spaces will be ready for occupancy in 18 months. If the expected time until the shopping center is
completed is estimated to be 15 months, with a standard deviation of 5 months, what is the
probability that the renters will not be able to occupy in 18 months? 11. The manager of the local National Video Store sells videocassette recorders at discount prices. If
the store does not have a video recorder in stock when a customer wants to buy one, it will lose the
sale because the customer will purchase a recorder from one of the many local competitors. The
problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet
all demand is excessively high. The manager has determined that if 85% of customer demand for
recorders can be met, then the combined cost of lost sales and inventory will be minimized. The
manager has estimated that monthly demand for recorders is normally distributed, with a mean of
175 recorders and a standard deviation of 55. Determine the number of recorders the manager
should order each month to meet 85% of customer demand.
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