Chapter 11 18. The following probabilities for grades in management science have been determined based on past records: Grade Probability
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18. The following probabilities for grades in management science have been determined based on past records:
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.
20. 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 Good Poor
A $900,000 -$800,000
B 120,000 70,000
Using the expected value of each investment alternative,determine which should be selected.
26. The weight of bags of fertilizer is normally distributed, with a mean of 50 pounds and a standard deviation of 6 pounds. What is the probability that a bag of fertilizer will weigh between 45 and 55 pounds?
28. The Polo Development Firm is building a shopping center.It has informed renters that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping center iscompleted is estimated to be 14 months,with a standard deviation of 4 months,what is the probability that the renters will not be able to occupy in 19 months?
30. 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 90% 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 of180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 90% of customer demand.