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Chapter 6: Q.58 (page 381)

Life insurance If four 21-year-old men are insured, the insurer’s 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,

μV=303.35

σV=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,

μx=303.35andσy=9707.57

Therefore,

μY=0.25μX1+0.25μX2+0.25μX3+0.25μX4=0.25×303.35+0.25×303.25+0.25×303.25+0.25×303.25=303.35

Compute the standard deviation ofV

σV=0.0625×9707.572+0.0625×9707.572+0.0625×9707.572=23559228.83=4853.79

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Most popular questions from this chapter

If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?

a. 0.25

b. 1.00

c. (41)(0.25)3(0.75)341(0.25)3(0.75)3

d. (41)(0.25)1(0.75)341(0.25)1(0.75)3

e.(0.75)3(0.75)1

Standard deviations (6.1) Continuous random variables A, B, and C all take values between 0 and 10 . Their density curves, drawn on the same horizontal scales, are shown here. Rank the standard deviations of the three random variables from smallest to largest. Justify your answer.

Take a spin An online spinner has two colored regions-blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is correct. Suppose we spin the spinner12 times and let X= the number of times it lands in the blue region. Make a graph of the probability distribution of X. Describe its shape.

Baby elk Refer to Exercise 77 . How surprising would it be for more than 4 elk in the sample to survive to adulthood? Calculate an appropriate probability to support your answer.

Ms. Hall gave her class a 10-question multiple-choice quiz.

LetX=the number of questions that a randomly selected student in the class answered correctly. The computer output gives information about the probability distribution of X. To determine each student’s grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5and then add 50. Let G=the grade of a randomly chosen student in the class.

More easy quiz

a. Find the mean of G.

b. Find the range of G.
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