   Chapter 6.2, Problem 56E ### 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 finding between a and b percent iron (in decimal form) in ore samples is modeled by P ( a ≤ x ≤ b ) = ∫ a b 2 x 3 e x 2 d x ,       0 ≤ a ≤ b ≤ 1. What is the probability of finding (a) between 0% and 25% and (b) between 50% and 100% iron in a sample?

(a)

To determine

To calculate: The probability of finding of iron between 0% and 25%, when probability finding of iron between a% and b% is modelled as P(axb)=ab2x3ex2dx.

Explanation

Given Information:

The probability finding of iron between a% and b% is modelled as P(axb)=ab2x3ex2dx.

Formula used:

The formula for the integral ueudu is;

ueudu=(u1)eu+C

The General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x2.

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

du=2xdx

Consider the provided expression:

P(axb)=ab2x3ex2dx

Rewrite.

P(axb)=ab(x2ex2)2xdx

Substitute u for x2, and du for 2xdx.

P(axb)=abueudu

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

P(axb)=[(u1)eu]ab

Substitute x2 for u

(b)

To determine

To calculate: The probability of finding of iron between 50% and 100%, when probability finding of iron between a% and b% is modelled as P(axb)=ab2x3ex2dx.

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