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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 first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

Define τ=χ+γ

The dealership’s 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’s 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,

μχ=1.1,σχ=0.943

μγ=0.7,σγ=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:

μB=500(1.1)+300(0.7)=760σB=500(0.943)2+300(0.64)2=509.09

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