# Probability and Decision Analysis

1. Use the normal approximation without the correction factor to find the probabilities in the following exercises.

a. In a binomial experiment with n = 300 and p=.5, find the probability that P is greater than 60%.

b. Repeat Part a with p = 55

c. Repeat Part a with p = .6

2. Determine the probability that in a sample of 100 the sample proportion is less than .75 if p=.80.

3. A commercial for a manufacturer of household appliances claims that 3% of all its products require a service call in the first year. A consumer protection association wants to check the claim by surveying 400 households that recently purchased one of the company's appliances. What is the probability that more than 5% require a service call within the first year? What would you say about the commercial's industry honesty if in a random sample of 400 households 5% report at least one service call?

4. The Red Lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is the probability that less than 70% rate the food as excellent?

5. A baker must decide how many specialty cakes to bake each morning. From past experience, she knows that the daily demand for cakes ranges from 0 to 3. Each cake costs $3.00 to produce and sells for $ 8.00 and any unsold cakes are thrown into the garbage at the end of the day.

a. Set up a payoff table to help the baker decide how many cakes to bake.

b. Set up the opportunity loss table.

c. Draw the decision tree.

6. Refer to Problem 5. Assume that the probability of each value of demand is the same for all possible demands.

a. Determine the EMV decision

b. Determine the EOL decision

7. The manager of a larger shopping center in Buffalo is in the process of deciding on the type of snow clearing service to hire for his parking lot. The two services are available. The White Christmas Company will clear all snowfalls for a flat fee of$40,000 for entire winter season. The Weplowen Company charges $18,000 for each snowfall it clears. Set up the payoff table to help the manager decide, assuming that the number of snowfalls per winter season ranges from 0 to 4.

8. Refer to Problem 7. Using subjective assessments, the manager has assigned the following probabilities to the number of snowfalls. Determine the optimal decision.

P(0) = .05 P(1) = .15 P(2) = .30 P(3)=.40 P(4)=.10

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This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.