   Chapter 6.2, Problem 55E ### 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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# Probability The probability of recalling between a and b percent (in decimal form) of the material learned in a memory experiment is modeled by P ( a ≤ x ≤ b ) = ∫ a b 75 14 ( x 4 + 5 x ) d x where 0 ≤ a ≤ b ≤ 1. What is the probability of recalling (a) between 40% and 80% and (b) between 0% and 50% of the material?

(a)

To determine

To calculate: The probability of recalling between 40% and 80%, when probability of recalling between a% and b% is modelled as P(axb)=ab7514(x4+5x)dx.

Explanation

Given Information:

The provided expression is,

P(axb)=ab7514(x4+5x)dx

Formula used:

The formula for the integral ua+budu is:

ua+budu=2(2abu)3b2a+bu+C

The General power differentiation Rule;

ddx[un]=nun1dudx

Calculation:

Consider u=x.

Differentiate the considered function with respect to x using power rule of differentiation.

du=dx

Consider the provided expression:

P(axb)=ab7514(x4+5x)dx

Rewrite.

P(axb)=7514abx4+5xdx

Here, a=4, b=5, u=x and du=dx.

Substitute u for x, a for 4, b for 5, and du for dx.

P(axb)=7514abua+budu

Use the formula of integration stated above and solve the above integral as;

P(axb)=7514[2(2abu)3b2a+bu]ab

Substitute x for u, 4 for a and 5 for b

(b)

To determine

To calculate: The probability of recalling between 0% and 50%, when probability of recalling between a% and b% is modelled as P(axb)=ab7514(x4+5x)dx.

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