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Chapter 6: Q.3.3 (page 373)

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 D=X-Y.

The dealership’s manager receives a 500bonus for each car sold and a300 bonus for each car leased. Find the mean and standard deviation of the difference in the manager’s bonus for cars sold and leased. Show your work.

Short Answer

Expert verified

From the given information, the mean and standard deviation are340 and509.09 respectively

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

02

Explanation

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

μB=500(1.1)−300(0.7)=340

σB=500(0.943)2+300(0.64)2=509.09

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Most popular questions from this chapter

18. Life insurance

(a) It would be quite risky for you to insure the life of a 21-year-old friend under the terms of Exercise 14. There is a high probability that your friend would live and you would gain \(1250in premiums. But if he were to die, you would lose almost \)100,000. Explain carefully why selling insurance is not risky for an insurance company that insures many thousands of 21-year-old men.

(b) The risk of an investment is often measured by the standard deviation of the return on the investment. The more variable the return is, the riskier the
investment. We can measure the great risk of insuring a single person’s life in Exercise 14by computing the standard deviation of the income Y that the insurer will receive. Find σY using the distribution and mean found in Exercise 14.

North Carolina State University posts the grade distributions for its courses online.3Students in Statistics 101in a recent semester received 26%A42%Bs,20%Cs,10%Ds,and2%Fs. Choose a Statistics 101student at random. The student’s grade on a four-point scale (with A=4) is a discrete random variable Xwith this probability distribution:

Sketch a graph of the probability distribution. Describe what you see .

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let χ= the number of cars sold and γ= the number of cars leased during the first hour of business on a randomly selected Friday. Based on previous records, the probability distributions of χand γare as follows:

Define τ=χ+γ

Compute στassuming that χ and γ are independent. Show your work.

Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below 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 10. Let G=the grade of a randomly chosen student in the class.

NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the median of G. Show your method.

(b) Find the IQR of G. Show your method.

(c) What shape would the probability distribution of Ghave? Justify your answer

The deck of 52cards contains 13hearts. Here is another wager: Draw one card at random from the deck. If the card drawn is a heart, you win 2. Otherwise, you lose 1. Compare this wager (call it Wager 2) with that of the previous exercise (call it Wager 1). Which one should you prefer?

(a) Wager 1, because it has a higher expected value.

(b) Wager 2, because it has a higher expected value.

(c) Wager 1, because it has a higher probability of winning.

(d) Wager 2, because it has a higher probability of winning. (e) Both wagers are equally favorable
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