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Page 354

Life insurance A life insurance company sells a term insurance policy to a21-year-old male that pays 100,000if the insured dies within the next 5years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of 250each year as payment for the insurance. The amount Y that the company earns on this policy is 250per year, less the 100,000that it must pay if the insured dies. Here is a partially completed table that shows information about risk of mortality and the values of Y=profit earned by the company:

(a) Copy the table onto your paper. Fill in the missing values of Y.

(b) Find the missing probability. Show your work.

(c) Calculate the mean μY. Interpret this value in context.


Page 349

Compute and interpret the standard deviation ofX.


Page 407

Knees Patients receiving artificial knees often experience pain after surgery. The pain is measured on a subjective scale with possible values of 1 (low) to 5 (high). Let X be the pain score for a randomly selected patient. The following table gives part of the probability distribution for X.





(a) Find P(X=5)

(b) If two patients who received artificial knees are chosen at random, what’s the probability that both of them report pain scores of 1or 2? Show your work.

(c) Compute the mean and standard deviation of X. Show your work.


Page 353

Toss 4times Suppose you toss a fair coin 4times. Let X=the number of heads you get.

(a) Find the probability distribution ofX.

(b) Make a histogram of the probability distribution. Describe what you see.

(c) Find P(X3) and interpret the result.


Page 409

What is the probability that a randomly chosen subject completes at least 3puzzles in the five-minute period while listening to soothing music?

(a) 0.3 (c) 0.6 (e) Cannot be determined

(b) 0.4 (d) 0.9


Page 354

Fire insurance Suppose a homeowner spends $300for a home insurance policy that will pay out $200,000if the home is destroyed by fire. Let Y=the profit made by the company on a single policy. From previous data, the probability that a home in this area will be destroyed by fire is 0.0002.

(a) Make a table that shows the probability distribution of Y.

(b) Compute the expected value of Y. Explain what this result means for the insurance company


Page 410

A test for extrasensory perception (ESP) involves asking a person to tell which of 5shapes—a circle, star, triangle, diamond, or heart—appears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4shapes incorrectly but gets the fifth correct?

a). 1/5

b). 454

c). 45415

d). 5145415


Q. 100

Page 406

Using Benford's law According to Benford's law (Exercise 5, page 353), the probability that the first digit of the amount of a randomly chosen invoice is an 8or a 9is 0.097. Suppose you examine randomly selected invoices from a vendor until you find one whose amount begins with an 8or a 9.

(a) How many invoices do you expect to examine until you get one that begins with an 8or 9? Justify your answer.

(b) In fact, you don't get an amount starting with an 8or 9until the 40thinvoice. Do you suspect that the invoice amounts are not genuine? Compute an appropriate probability to support your answer.

Q. 101

Page 406

101. Job reads that 1 out of 4 eggs contains salmonella bacteria. So he never uses more than 3 eggs in cooking. If eggs do or don't contain salmonella independently of each other, the number of contaminated eggs when Joe uses 3 chosen at random has the following distribution:

(a) binomial; n=4andp=1/4

(b) binomial; n=3andp=1/4

(c) binomial; n=3andp=1/3

(d) geometric;p=1/4

(e) geometric;p=1/3

Q. 102

Page 406

In the previous exercise, the probability that at least 1of Joe's 3eggs contains salmonella is about

(a) 0.84.

(b) 0.68.

(c) 0.58.

(d) 0.42.

(e) 0.30.

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