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Chapter 6: Q.58 (page 381)

Life insurance If four 21-year-old men are insured, the insurer鈥檚 average income is

V=X1+X2+X3+X44=0.25X1+0.25X2+0.25X3+0.25X4

where Xiis the income from insuring one man. Assuming that the amount of income earned on individual policies is independent, find the mean and standard deviation of V. (If you compare with the results of Exercise 57, you should see that averaging over more insured individuals reduces risk.)

Short Answer

Expert verified

The mean and standard deviation,

渭V=303.35

蟽V=4853.79

Step by step solution

01

Given Information

Given in the question that the average income of the insures is

V=X1+X2+X3+X44=0.25X1+0.25X2+0.25X2+0.25X4

02

Calculate the mean and standard deviation of V

Let's compute the mean of V

Here,

渭x=303.35and蟽y=9707.57

Therefore,

渭Y=0.25渭X1+0.25渭X2+0.25渭X3+0.25渭X4=0.25脳303.35+0.25脳303.25+0.25脳303.25+0.25脳303.25=303.35

Compute the standard deviation ofV

蟽V=0.0625脳9707.572+0.0625脳9707.572+0.0625脳9707.572=23559228.83=4853.79

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Most popular questions from this chapter

A company鈥檚 single-serving cereal boxes advertise 1.63ounces of cereal. In fact, the amount of cereal X in a randomly selected box can be modeled by a Normal distribution with a mean of 1.70ounces and a standard deviation of 0.03ounce. Let Y=the excess amount of cereal beyond what鈥檚 advertised in a randomly selected box, measured in grams (1ounce=28.35grams).

a. Find the mean of Y.

b. Calculate and interpret the standard deviation of Y.

c. Find the probability of getting at least 1grammore cereal than advertised.

1 in 6 wins As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside of each bottle cap. Some of the caps said, "Please try again!" while others said, "You're a winner!" The company advertised the promotion with the slogan " 1 in 6 wins a prize." Grayson's statistics class wonders if the company's claim holds true at a nearby convenience store. To find out, all 30 students in the class go to the store and each huys one 20-ounce bottle of the soda.

a. Find the probability that two or fewer students would win a prize if the company's claim is true.

b. Two of the students in Grayson's class got caps that say, "You're a winner!" Does this result give convincing evidence that the company's 1-in-6 claim is false?

Total gross profits G on a randomly selected day at Tim鈥檚 Toys follow a distribution that is approximately Normal with mean \(560 and standard deviation \)185. The cost of renting and maintaining the shop is $65 per day. Let P=profit on a randomly selected day, so P=G鈭�65. Describe the shape, center, and variability of the probability distribution of P.

.Life insurance The risk of insuring one person鈥檚 life is reduced if we insure many people. Suppose that we insure two 21-year-old males, and that their ages at death are independent. If X1andX2are the insurer鈥檚 income from the two insurance policies, the insurer鈥檚 average income W on the two policies is

W=X1+X22=0.5X1+0.5X2

Find the mean and standard deviation of W. (You see that the mean income is the same as for a single policy but the standard deviation is less.)

Taking the train According to New Jersey Transit, the 8:00A.M. weekday train from Princeton to New York City has a 90%chance of arriving on time on a randomly selected day. Suppose this claim is true. Choose 6 days at random. Let localid="1654594369074" Y=the number of days on which the train arrives on time.
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