Discussion:
1 A gambler in Las Vegas is cutting a deck of cards for $1,000. What is the probability that the cards for the gambler will be the follow?
1. A face card
2. A queen
3. A Spade
4. A jack of spades
2 The life of an electronic transistor is normally distributed, with a mean of 500 hour' deviation of 80 hours. Determine the probability that a transistor will last for more than 400 hours.
3 The Polo Development Firm is building a shopping center. 1t has informed renters that their rental spaces will be ready for occupancy in 19 months. If the expected time until the shopping center is completed 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?
4 A manufacturing company has 10 machines in continuous operation during a workday. The probability that an individual machine will break down during the day is .10. Determine the probability that during any given day 3 machines will break down.
5 The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.
6 A concessions manager at the Tech versus A&M football game must decide whether to have the vendors sell sun visors or umbrellas. There is a 30% chance of rain, a 15% chance of overcast skies, and a 55% chance of sunshine, according to the weather forecast in College Junction, where the game is to be held. The manager estimates that the following profits will result from each decision, given each set of weather conditions:
Weather Conditions
Decision Rain Overcast Sunshine
. 30 .15 .55
Sun visors $-500 $-200 $1,500
Umbrellas 2,000 0 -900
1. Compute the expected value for each decision and select the best one.
2. Develop the opportunity loss table and compute the expected opportunity loss for each decision.