### MAT 119 8.2 Expected Value & Odds

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TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Records kept by the chief dietitian at the university cafeteria over a 37-period show the following weekly consumption of milk (in gallons).

Milk 200 205 210 215 220 225 230 235 240

Weeks 4 5 6 2 5 4 5 5 1

(a) Find the average number of gallons of milk consumed per week in the cafeteria. (Round your answer to the nearest whole number.)

(b) Let the random variable X denote the number of gallons of milk consumed in a week at the cafeteria. Find the probability distribution of the random variable X. (Round your answers to three decimal places.)

Milk200205210215220225230235240TOTAL

Weeks45625455137

P(X=x)0.1080.1350.1620.0540.1350.1080.1350.1350.027

Compute E(X), the expected value of X. (Round your answer to the nearest whole number.)

E(X) =

1. On the basis of past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy 0, 1, 2, 3, or 4 DVDs. How many DVDs can a customer entering this store be expected to buy? (Enter your answer to two decimal places.)

DVDs 0 1 2 3 4

Probability 0.40 0.37 0.15 0.06 0.02

1. The management of the Cambridge Company has projected the sales of its products (in millions of dollars) for the upcoming year, with the associated probabilities shown in the following table.

Sales 16 19 22 25 28 31

Probability 0.02 0.11 0.38 0.31 0.14 0.04

What does the management expect the sales to be next year? (Enter your answer to two decimal places.)

1. A panel of 69 economists was asked to predict the average unemployment rate for the upcoming year. The results of the survey follow.

Unemployment Rate, % 9.6 9.9 10.2 10.5 10.8 11.1 11.4

Economists 2 6 8 21 14 13 5

On the basis of this survey, what does the panel expect the average unemployment rate to be next year? (Round your answer to two decimal places.)

1. A man wishes to purchase a 5-year term-life insurance policy that will pay the beneficiary \$20,000 in the event that the man's death occurs during the next 5 years. Using life insurance tables, he determines that the probability that he will live another 5 years is 0.96. What is the minimum amount that he can expect to pay for his premium? Hint: The minimum premium occurs when the insurance company's expected profit is zero.

2. The proprietor of Midland Construction Company has to decide between two projects. He estimates that the first project will yield a profit of \$190,000 with a probability of 0.6 or a profit of \$140,000 with a probability of 0.4; the second project will yield a profit of \$240,000 with a probability of 0.4 or a profit of \$90,000 with a probability of 0.6.

Find the expected profit for each project.

first project

second project

Which project should the proprietor choose if he wants to maximize his expected profit?

first project

second project

1. Suppose the probability that it will rain tomorrow is 0.4.

(a) What are the odds that it will rain tomorrow?

(b) What are the odds that it will not rain tomorrow?

1. The probability of an event E occurring is 0.9. What are the odds in favor of E occurring?

What are the odds against E occurring?

1. The odds in favor of an event E occurring are 9 to 5. What is the probability of E occurring? (Round your answer to three decimal places.)

P(E) =

1. The frequency distribution of the hourly wage rates (in dollars) among blue-collar workers in a certain factory is given in the following table. Find the mean (or average) wage rate, the mode, and the median wage rate of these workers. (If necessary, round your answers to two decimal places.)

mean

mode

median

Wage Rate 14.10 14.20 14.30 14.40 14.50 14.60

Frequency 60 90 75 120 60 45

1. In an examination given to a class of 20 students, the following test scores were obtained.

45 45 50 50 55 60 70 75 75 80

80 85 85 85 85 90 90 95 95 100

(a) Find the mean (or average) score, the mode, and the median score.

mean

mode

median

(b) Which of these three measures of central tendency do you think is the least representative of the set of scores?

mean

mode

median

1. The normal daily minimum temperature in degrees Fahrenheit for the months of January through December in a certain city are given below.

46.6 48.4 48.6 49.2 50.3 52.5

53.1 54.2 55.8 54.8 51.4 47.2

Find the average and the median daily temperature in the city for these months. (Round your answers to one decimal place.)

average F

median F

1. The weights, in ounces, of ten packages of potato chips are given below.

14.1 14 13.8 14 13.9 14.1 13.9 14 14 14.2

Find the average and the median of these weights.

average oz

median oz

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