Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q82E (page 248)

Waiting for a car wash. An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that 30 minutes before closing time, 5 cars are in line. If the car wash is in continuous use until closing time, will anyone likely be in line at closing time?

Short Answer

Expert verified

The probability of no car will be a washis likely that someone will be in line.

Step by step solution

01

Given information

x denotes the number of cars that arrive at the car wash in 30-minute intervals.

x follows a Poisson distribution with a mean of 5.

02

Calculate the probability

Let x denote the number of cars that arrive at the car wash in 30-minute intervals. On average 10 cars per hour arrive at the car wash.

Therandom variable x follows a Poisson distribution with parameter,

λ=10  per  houre=10×3060  per  30  minutes=5  per  30  minutes

The probability mass function of x is given by,

PX=x=e-λλxx!, x=0,1,2,...=e-55xx!, x=0,1,2,...

The probability of x is less than one is,

Px<1=Px=0=e-5500!=0.006738≈0.0067

Px<1=0.0067

Therefore, the probability that no car will be a wash is likely someone will be in line.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the following probabilities for the standard normal

random variable z:

a.P(z≤2.1)

b.P(z≥2.1)

c.P(z≥-1.65)

d.P(-2.13≤z≤-.41)

e.P(-1.45≤z≤2.15)

f.P(z≤-1.43)

Errors in measuring truck weights. To help highway planners anticipate the need for road repairs and design futureconstruction projects, data are collected on the estimatedvolume and weight of truck traffic on specific roadways (Transportation Planning Handbook, 2016) using specialized “weigh-in-motion” equipment. In an experiment involving repeated weighing of a 27,907-pound truck, it wasfound that the weights recorded by the weigh-in-motionequipment were approximately normally distributed witha mean of 27,315 and a standard deviation of 628 pounds

(Minnesota Department of Transportation). It follows thatthe difference between the actual weight and recordedweight, the error of measurement, is normally distributedwith a mean of 592 pounds and a standard deviation of 628pounds.

a. What is the probability that the weigh-in-motion equipment understates the actual weight of the truck?

b. If a 27,907-pound truck was driven over the weigh-in-motion equipment 100 times, approximately howmany times would the equipment overstate the truck’sweight?

c. What is the probability that the error in the weightrecorded by the weigh-in-motion equipment for a27,907-pound truck exceeds 400 pounds?

d. It is possible to adjust (or calibrate) the weigh-in-motion equipment to control the mean error of measurement. At what level should the mean error beset so the equipment will understate the weight of a27,907-pound truck 50% of the time? Only 40% of thetime

If x is a binomial random variable, use Table I in Appendix D to find the following probabilities:

a.for n = 10, p = .4

b.for n = 15, p = .6

c.for n = 5, p = .1

d.for n = 25, p = .7

e.for n = 15, p = .9

f.for n = 20, p = .2

Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, Exercise 3.109 (p. 204). Recall that each of 124 college students selected showroom displays for portable grills. Five different displays (representing five different-sized grills) were available. Still, the students were instructed to select only three displays to maximize purchases of Grill #2 (a smaller-sized grill). The table shows the grill display combinations and the number of times each was selected by the 124 students. Suppose one of the 124 students is selected at random. Let x represent the sum of the grill numbers selected by this student. (This value indicates the size of the grills selected.)

a. Find the probability distribution for x.

b. What is the probability that x exceeds 10?

178 Dutch elm disease. A nursery advertises that it has 10 elm treesfor sale. Unknown to the nursery, 3 of the trees have already been infected with Dutch elm disease and will die withina year.

a. If a buyer purchases 2 trees, what is the probability that bothtrees will be healthy?

b. Refer to part a. What is the probability that at least 1 of thetrees is infected?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free