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Chapter 5: Problem 68

A company that offers roadside assistance to drivers reports that the probability that a call for assistance will be to help someone who is locked out of his or her car is \(0.18 .\) Give a relative frequency interpretation of this probability.

Short Answer

Expert verified
In the long term, the company can expect about 18% of all their calls, or 18 out of every 100 calls, to be from people locked out of their cars.

Step by step solution

01

Understand the concept of relative frequency

Relative frequency gives a measure of the number of times a particular event occurs as a fraction of the total number of trials. It's often used as an estimate of probability. To attach a meaning to the abstract concept of probability in this case, we must talk in terms of the large number of trials.
02

Apply relative frequency to the given exercise

In this context, the given probability 0.18 means that if the company keeps receiving calls for assistance under the same conditions, then in the long run, about 18% of all calls or 18 out of every 100 calls will be from people who have locked themselves out of their cars.

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Most popular questions from this chapter

An appliance manufacturer offers extended warranties on its washers and dryers. Based on past sales, the manufacturer reports that of customers buying both a washer and a dryer, \(52 \%\) purchase the extended warranty for the washer, \(47 \%\) purchase the extended warranty for the dryer, and \(59 \%\) purchase at least one of the two extended warranties. a. Use the given probability information to set up a "hypothetical 1000 " table. b. Use the table from Part (a) to find the following probabilities: i. the probability that a randomly selected customer who buys a washer and a dryer purchases an extended warranty for both the washer and the dryer. ii. the probability that a randomly selected customer purchases an extended warranty for neither the washer nor the dryer.

Suppose you want to estimate the probability that a randomly selected customer at a particular grocery store will pay by credit card. Over the past 3 months, 80,500 payments were made, and 37,100 of them were by credit card. What is the estimated probability that a randomly selected customer will pay by credit card?

An airline reports that for a particular flight operating daily between Phoenix and Atlanta, the probability of an on-time arrival is \(0.86 .\) Give a relative frequency interpretation of this probability.

Consider the following events: \(C=\) event that a randomly selected driver is observed to be using a cell phone \(A=\) event that a randomly selected driver is observed driving a car \(V=\) event that a randomly selected driver is observed driving a van or SUV \(T=\) event that a randomly selected driver is observed driving a pickup truck Based on the article "Three Percent of Drivers on Hand-Held Cell Phones at Any Given Time" (San Luis Obispo Tribune, July 24,2001 ), the following probability estimates are reasonable: \(P(C)=0.03, P(C \mid A)=0.026, P(C \mid V)=0.048\) and \(P(C \mid T)=0.019 .\) Explain why \(P(C)\) is not just the average of the three given conditional probabilities.

Roulette is a game of chance that involves spinning a wheel that is divided into 38 equal segments, as shown in the accompanying picture. A metal ball is tossed into the wheel as it is spinning, and the ball eventually lands in one of the 38 segments. Each segment has an associated color. Two segments are green. Half of the other 36 segments are red, and the others are black. When a balanced roulette wheel is spun, the ball is equally likely to land in any one of the 38 segments. a. When a balanced roulette wheel is spun, what is the probability that the ball lands in a red segment? b. In the roulette wheel shown, black and red segments alternate. Suppose instead that all red segments were grouped together and that all black segments were together. Does this increase the probability that the ball will land in a red segment? Explain. c. Suppose that you watch 1000 spins of a roulette wheel and note the color that results from each spin. What would be an indication that the wheel was not balanced?
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