   Chapter 9.2, Problem 29E ### 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
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# Waiting Time Buses arrive and depart from a college every 30 minutes. The probability density function for the waiting time t (in minutes) for a person arriving at the bus stop is f ( t ) = 1 30 , [ 0 , 30 ] .Find the probability that the person will wait (a) no more than 5 minutes and (b) at least 18 minutes.

(a)

To determine

To calculate: The probability that a person, who is waiting for the bus not more than 5 minutes. Where the probability density for the waiting time t (in minute) for a man who is arriving at the bus stop is represented by the function f(t)=130, [0,30] here, the frequency of the bus is 30 minutes.

Explanation

Given Information:

The probability density for the waiting time t (in minute) for a man who is arriving at the bus stop is represented by the function f(t)=130, [0,30] here, the frequency of the bus is 30 minutes.

Formula used:

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

P(ctd)=cdf(t) dt

Calculation:

Consider the provided probability density function,

f(t)=130, [0,30]

Since, the person is not waiting for the bus more than 5 minutes therefore,

The interval in which probability lies is 0t5.

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

(b)

To determine

To calculate: The probability that a person, who is waiting for the bus at least 18 minutes. Where the probability density for the waiting time t (in minute) for a man who is arriving at the bus stop is represented by the function f(t)=130, [0,30] here, the frequency of the bus is 30 minutes.

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