   Chapter 6, Problem 34RE ### 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 locating between a and b percent of the oil and gas deposits (in decimal form) in a region is modeled by P ( a ≤ x ≤ b ) = ∫ a b 1.5 x 2 e x 1.5   d x ,     0 ≤ a ≤ b ≤ 1. What is the probability of locating (a) between 40% and 60% and (b) between 0% and 50% of the deposits?

(a)

To determine

To calculate: The probability of locating oil and gas between 40% and 60%, when probability locating oil and gas between a% and b% is modelled as P(axb)=ab1.5x2ex1.5dx.

Explanation

Given Information:

The probability locating oil and gas between a% and b% is modelled as,

P(axb)=ab1.5x2ex1.5dx

Formula used:

The integral formula,

ueudu=(u1)eu+C

General power differentiation Rule,

ddx[un]=nun1dudx

Calculation:

Consider the provided data,

The probability locating oil and gas between a% and b% is modelled as

P(axb)=ab1.5x2ex1.5dx

Let, u=x1.5

Differentiate u=x1.5 with respect to x by the use of power rule of differentiation.

du=1.5x0.5dx

Consider the provided expression:

P(axb)=ab1.5x2ex1.5dx

And rewrite as.

P(axb)=ab(x1.5ex1.5)1.5x0.5dx

Compare the expression from the formula,

ueudu

Substitute u for x1.5, and du for 1

(b)

To determine

To calculate: The probability of locating oil and gas between 0% and 50%, when probability locating oil and gas between a% and b% is modelled as P(axb)=ab1.5x2ex1.5dx.

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