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Chapter 6: Q.1.2 (page 362)

A large auto dealership keeps track of sales made during each hour of the day. Let X= the number of cars sold during the first hour of business on a randomly selected Friday. Based on previous records, the probability distribution of Xis as follows:

The random variable Xhas mean μX=1.1and standard deviation σX=0.943.

To encourage customers to buy cars on Friday mornings, the manager spends 75to provide coffee and doughnuts. The manager’s net profit Ton a randomly selected Friday is the bonus earned minus this 75. Find the mean and standard deviation ofT.

Short Answer

Expert verified

From the given information, the required mean and standard deviation are 475and 471.50respectively.

Step by step solution

01

Given Information

Given in the question that,

The random variable Xhas mean μX=1.1

The standard deviation σX=0.943

The manager spends 75to provide coffee and doughnuts

02

Step 2: Explanation

The function of Tis :

T=Y-75

The mean and standard deviation of Tcan be calculated as:

localid="1649912551282" μT=μ75−μ(75)=550−75=475σT=σY−75=σY=471.50

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