   Chapter 6, Problem 33RE ### 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 96 11 ( x 9 + 16 x ) d x , where 0   ≤   a   ≤   b   ≤ 1 . What is the probability of recalling (a) between 0% and 80% and (b) between 0% and 50% of the material?

(a)

To determine

To calculate: The probability of recalling between 0% and 80%, when probability of recalling between a% and b% is modelled as P(axb)=ab9611(x9+16x)dx.

Explanation

Given Information:

Probability of recalling between a% and b% is modelled as,

P(axb)=ab9611(x9+16x)dx

Formula used:

The integral formula,

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

General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider the provided data,

Probability of recalling between a% and b% is modelled as

P(axb)=ab9611(x9+16x)dx

Let, u=x

Differentiate u=x with respect to x by the use of power rule of differentiation.

du=dx

Consider the provided expression,

P(axb)=ab9611(x9+16x)dx

And rewrite the integral as.

P(axb)=9611ab(x9+16x)dx

Now, compare the integral with the formula,

ua+budu

Here, a=9, b=16, u=x and du=dx

(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)=ab9611(x9+16x)dx.

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