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Chapter 6: Q.2.3 (page 370)

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

顿别铿乶别 蟿=蠂+纬

The dealership鈥檚 manager receives a 500bonus for each car sold and a 300 bonus for each car leased. Find the mean and standard deviation of the manager鈥檚 total bonus B. Show your work.

Short Answer

Expert verified

From the given information, the mean and standard deviation are 760and 509.09respectively.

Step by step solution

01

Given Information

It is given in the question that,

渭蠂=1.1,蟽蠂=0.943

渭纬=0.7,蟽纬=0.64

The manager receives a bonus of 500for each sold car and 300for each car sold.

02

Explanation

The mean and standard deviation of the total bonus of the manager can be calculated as:

渭B=500(1.1)+300(0.7)=760蟽B=500(0.943)2+300(0.64)2=509.09

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Most popular questions from this chapter

Benford鈥檚 law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1to 9. In that case, the first digit Yof a randomly selected expense amount would have the probability distribution shown in the histogram.

(a). Explain why the mean of the random variable Y is located at the solid red line in the figure.

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