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Chapter 6: Q.27 (page 356)

A housing company builds houses with two-car garages. What percent of households have more cars than the garage can hold? (a) 13%

(b) 20%

(c) 45%

(d) 55%

(e) 80%

Short Answer

Expert verified

The percent of households have more cars than the garage can hold is option (b)20%.

Step by step solution

01

Given Information

The probability model if we ignore the few households that own more than 5 cars.

02

Explanation

We must calculate the percentage of homes with more cars than the (two-car) garage can accommodate, which equals toX>2

Add the corresponding probabilities:

localid="1649915803257" P(X>2)=P(X=3)+P(X=4)+P(X=5)=0.13+0.05+0.02=0.20=20%

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Most popular questions from this chapter

49. Checking independence In which of the following games of chance would you be willing to assume independence of Xandlocalid="1649903939419" Y in making a probability model? Explain your answer in each case.
(a) In blackjack, you are dealt two cards and examine the total points localid="1649903945891" Xon the cards (face cards count localid="1649903950298" 10points). You can choose to be dealt another card and compete based on the total pointslocalid="1649903956461" Y on all three cards.
(b) In craps, the betting is based on successive rolls of two dice. localid="1649903966379" Xis the sum of the faces on the first roll, and localid="1649903971075" Yis the sum of the faces on the next roll.

A deck of cards contains 52cards, of which 4are aces. You are offered the following wager: Draw one card at random from the deck. You win \(10if the card drawn is an ace. Otherwise, you lose \)1. If you make this wager very many times, what will be the mean amount you win?

(a) About 鈭�\(1, because you will lose most of the time.

(b) About \)9, because you win \(10but lose only \)1.

(c) About 鈭�\(0.15; that is, on average you lose about 15cents. (d) About \)0.77; that is, on average you win about 77cents.

(e) About $0, because the random draw gives you a fair bet.

Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made 80%of his field-goal attempts in the past. This season he attempts 20field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made 80%of his free-throw attempts in the past. This season he takes 150free throws. Basketball free throws are always attempted from 15feet away with no interference from other players

A small ferry runs every half hour from one side of a large river to the other. The number of cars Xon a randomly chosen ferry trip has the probability distribution shown below. You can check that 渭X=3.87and 蟽X=1.29.

(a) The cost for the ferry trip is $5. Make a graph of the probability distribution for the random variable M=money collected on a randomly selected ferry trip. Describe its shape.

(b) Find and interpret 渭M.

(c) Compute and interpret 蟽M.

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.
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