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Chapter 8: Q. 8.1 (page 393)

The number of automobiles sold weekly at a certain dealership is a random variable with an expected value of16. Give an upper bound to the probability that

(a)next week鈥檚 sales exceed18;

(b)next week鈥檚 sales exceed25.

Short Answer

Expert verified

(a)P{X>18}鈮�E[X]18=89=.89(b)P{X>25}鈮�E[X]25=1625=.64

Step by step solution

01

Given Information.

The number of automobiles sold weekly at a certain dealership is a random variable with an expected value of16.

02

Part (a) Explanation.

Let the random variableXrepresent the number of automobiles sold (in a week). It is given thatE[X]=16.

By Markov's inequality, we get:

P{X>18}鈮�E[X]18=1618=89=.89

03

Part (b) Explanation.

P{X>25}鈮�E[X]25=1625=1625=.64

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Most popular questions from this chapter

An insurance company has 10,000automobile policyholders. The expected yearly claim per policyholder is240a standard deviation of800. Approximate the probability that the total yearly claim exceeds 2.7a million.

It Xis a gamma random variable with parameters(n,1), approximately how large must nbe so thatPXn-1>.01<.01?

Explain why a gamma random variable with parameters(t,位)has an approximately normal distribution whentis large.

8.6 . In Self-Test Problem 8.5, how many components would one need to have on hand to be approximately 90percent certain that the stock would last at least 35days?

Suppose in Problem 8.14that the variance of the number of automobiles sold weekly is9.

(a)Give a lower bound to the probability that next week鈥檚 sales are between 10and22, inclusively.

(b)Give an upper bound to the probability that next week鈥檚 sales exceed18.
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