/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q82E Waiting for a car wash. An autom... [FREE SOLUTION] | 91影视

91影视

Log out

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,

位=10鈥�鈥�per鈥�鈥�houre=10脳3060鈥�鈥�per鈥�鈥�30鈥�鈥�minutes=5鈥�鈥�per鈥�鈥�30鈥�鈥�minutes

The probability mass function of x is given by,

PX=x=e-位位xx!,鈥�x=0,1,2,...=e-55xx!,鈥�x=0,1,2,...

The probability of x is less than one is,

Px<1=Px=0=e-5500!=0.006738鈮�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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

The binomial probability distribution is a family of probability distributions with every single distribution depending on the values of n and p. Assume that x is a binomial random variable with n = 4.

  1. Determine a value of p such that the probability distribution of x is symmetric.
  2. Determine a value of p such that the probability distribution of x is skewed to the right.
  3. Determine a value of p such that the probability distribution of x is skewed to the left.
  4. Graph each of the binomial distributions you obtained in parts a, b, and c. Locate the mean for each distribution on its graph.\
  5. In general, for what values of p will a binomial distribution be symmetric? Skewed to the right? Skewed to the left?

If a population data set is normally distributed, what isthe proportion of measurements you would expect to fallwithin the following intervals?

a.渭卤蟽b.渭卤2蟽c.渭卤3蟽

Maintaining pipe wall temperature. Maintaining a constant pipe wall temperature in some hot-process applications is critical. A technique that utilizes bolt-on trace elements to maintain temperature was presented in the Journal of Heat Transfer (November 2000). Without bolt-on trace elements, the pipe wall temperature of a switch condenser used to produce plastic has a uniform distribution ranging from 260掳 to 290掳F. When several bolt-on trace elements are attached to the piping, the wall temperature is uniform from 278掳 to 285掳F.

a. Ideally, the pipe wall temperature should range between 280掳 and 284掳F. What is the probability that the temperature will fall in this ideal range when no bolt-on trace elements are used? When bolt-on trace elements are attached to the pipe?

b. When the temperature is 268掳F or lower, the hot liquid plastic hardens (or plates), causing a buildup in the piping. What is the probability of plastic plating when no bolt-on trace elements are used? When bolt-on trace elements are attachedto the pipe?

Hospital patient interarrival times. The length of time between arrivals at a hospital clinic has an approximately exponential probability distribution. Suppose the mean time between arrivals for patients at a clinic is 4 minutes.

a. What is the probability that a particular interarrival time (the time between the arrival of two patients) is less than 1 minute?

b. What is the probability that the next four interarrival times are all less than 1 minute?

c. What is the probability that an interarrival time will exceed 10 minutes?

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
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.