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Chapter 3: Q71E (page 196)

Ambulance response time.Geographical Analysis(Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario. An ambulance station has one vehicle and two demand locations, A and B. The probability that the ambulance can travel to a location in under 8 minutes is .58 for location A and .42 for location B. The probability that the ambulance is busy at any point in time is .3.

a.Find the probability that EMS can meet the demand for an ambulance at location A.

b.Find the probability that EMS can meet the demand for an ambulance at location B.

Short Answer

Expert verified
  1. 0.406
  2. 0.294

Step by step solution

01

 Step 1: Given

Let P (Busy) be the probability that the ambulance is busy.

Therefore, let P (Free) be the probability that the ambulance is free

P (A) is the probability that the ambulance reaches location A on time

P (B) is the probability that the ambulance reaches location B on time

02

Finding the probability that EMS can meet the demand for an ambulance at location A.

The probability of the ambulance reaching location A on time is dependent on whether it is free and the time.

P(A)=P(A|Free)脳笔(Free)=0.58脳0.7=0.406

Therefore, P(A) = 0.406.

03

Finding the probability that EMS can meet the demand for an ambulance at location B.

Following the same logic as above,

P(B)=P(B|Free)脳笔(Free)=0.42脳0.7=0.294

Therefore, the probability that the ambulance reaches location B on time is 0.294.

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Most popular questions from this chapter

Who prepares your tax return? As part of a study on income tax compliance (Behavioral Research and Accounting, January 2015), researchers sampled 270 adults at a shopping mall and asked each: 鈥淲ho usually prepares your tax return?鈥� Their answers (and frequency of responses) are shown in the table (p. 170). Use the information in the table to estimate the probability that a randomly selected adult uses a friend, relative, or professional to prepare his or her income tax return.

Table for Exercise 3.16

Response

Frequency

You

100

Your spouse

16

Equally with spouse

7

Friend or relative

31

Professional help

114

Not required to file

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270

Source: S. Bhattacharjee, K. Moreno, and D. Salbador, 鈥淭he Impact of Multiple Tax Returns on Tax Compliance Behavior,鈥� Behavioral Research and Accounting, Vol. 27, No. 1, January 2015 (from Table 1).

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was evaluated for each of three different years (growing seasons) by a wine-tasting panel. Based on the taste tests, the panel (as a group) selected the wine with the highest quality.

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c.If the wines were all of equal quality, what is the probability that the panel selected a wine produced in year 3 as the wine with the highest quality?

d.The panel consisted of four different wine tasters who performed the evaluations independently of each other. If the wines were all of equal quality, what is the probability that all four tasters selected a Llarga wine as the wine with the highest quality?

Do social robots walk or roll?Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercises 3.10 (p. 168) and 3.37 (p. 181). Recall that in a random sample of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. If a social robot is designed with wheels, what is the probability that the robot also has legs?

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Suppose you鈥檙e on a game show, and you鈥檙e given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a door鈥攕ay, #1鈥攁nd the host, who knows what鈥檚 behind the doors, opens another door鈥攕ay #3鈥攚hich has a goat. He then says to you, 鈥淒o you want to pick door #2?鈥� Is it to your advantage to switch your choice?

Marilyn鈥檚 answer: 鈥淵es, you should switch. The first door has a 13 chance of winning [the car], but the second has a 23 chance [of winning the car].鈥� Predictably, vos Savant鈥檚 surprising answer elicited thousands of criticalletters, many of them from PhD mathematicians, who disagreed with her. Who is correct, the PhDs or Marilyn?

Testing a watch manufacturer鈥檚 claim. A manufacturer of a new Smart Watch claims that the probability of its watch running more than 1 minute slow or 1 minute fast after 1 year of use is .05. A consumer protection agency has purchased four of the manufacturer鈥檚 watches with the intention of testing the claim.

  1. Assuming that the manufacturer鈥檚 claim is correct, what is the probability that none of the watches are as accurate as claimed?
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