   Chapter 13.2, Problem 65E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Testing The time t (in minutes) needed to read an article appearing on a foreign-language placement test is given by the probability density function f ( t ) =   0.012 t 2 − 0.0012 t 3 ,         0   ≤ t ≤ 10 For a test taker chosen at random, find the probability that this person takes 8 minutes or more to read the article.

To determine

To calculate: The probability that the person takes 8 minutes or more to read the article where time t in minutes needed to read an article which appears on a foreign language placement test and is given by the probability density function f(t)=0.012t20.0012t3, 0t10 .

Explanation

Given Information:

The probability density function f(t)=0.012t20.0012t3.

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral xndx=xn+1n+1.

Calculation:

Consider the probability density function f(t)=0.012t20.0012t3.

Since, the person takes 8 minutes or more to read the article and 0t10, total time taken is the definite integral from 8 to 10.

Thus, probability that the person takes 8 minutes or more is the integral 810(0.012t20.0012t3)dt.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Simplify the integral by the use of the formula xndx=xn+1n+1.

810(0.012t20.0012t3)dt=(0.012t2+12+10.0012t3+13+1)810=(0

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