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Mathematical Applications for the ...

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

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BuyFindarrow_forward

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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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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