   Chapter 9.2, Problem 33E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Using the Exponential Density Function In Exercises 33-36, find the required probabilities using the exponential probability density function f ( t ) = 1 λ e − t λ , [ 0 , ∞ ) .Waiting Time The waiting time t (in minutes) for service at the checkout at a grocery store is exponentially distributed with λ   =   3 . Find the probability of waiting (a) less than 2 minutes, (b) more than 2 minutes but less than 4 minutes, and (c) at least 2 minutes.

(a)

To determine

To calculate: The probability of waiting less than 2 minutes. If the waiting time is exponentially distributed by the density function, f(t)=1λetλ, [0,), where t(in minutes) represents the time waiting time and λ=3.

Explanation

Given Information:

The waiting time is exponentially distributed by the density function, f(t)=1λetλ, [0,), where t(in minutes) represents the time waiting time and λ=3.

Formula used:

If f is function of a continuous random variable t, then the probability that t lies in the interval [c,d] is,

P(ctd)=cdf(t) dt

Calculation:

Consider the provided probability density function,

f(t)=1λetλ, [0,), and λ=3

Since, the waiting time is less than 2 minutes. therefore,

The interval in which probability lies is 0<t<2.

Now, apply the formula of probability P(ctd)=cdf(t) dt.

Substitute the values 0 for c, 2 for d and 1λetλ for f(t) in the above formula as,

P(0<t<2)=0213et3 dt as the value of the λ is 3

(b)

To determine

To calculate: The probability of waiting more than 2 minutes but less than 4 minutes. If the waiting time is exponentially distributed by the density function, f(t)=1λetλ, [0,), where t(in minutes) represents the time waiting time and λ=3.

(c)

To determine

To calculate: The probability of waiting at least 2 minutes. If the waiting time is exponentially distributed by the density function, f(t)=1λetλ, [0,), where t(in minutes) represents the time waiting time and λ=3.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Define sampling with replacement and explain why is it used?

Statistics for The Behavioral Sciences (MindTap Course List)

#### In problems 27-30, find. 28.

Mathematical Applications for the Management, Life, and Social Sciences

#### Using differentials, an approximation to (3.04)3 is: 28.094464 28.08 28.04 28

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 