   # Finding a Probability In Exercises 31-36, sketch the graph of the probability density function over the indicated interval and find each probability. f ( x ) = 3 128 x , [ 0 , 16 ] (a) P ( 4 &lt; x &lt; 9 ) (b) P ( 4 &lt; x &lt; 16 ) (c) P ( x &lt; 9 ) (d) P ( 0 &lt; x &lt; 12 ) ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 36RE
Textbook Problem
1 views

## Finding a Probability In Exercises 31-36, sketch the graph of the probability density function over the indicated interval and find each probability. f ( x ) = 3 128 x , [ 0 , 16 ] (a) P ( 4 < x < 9 ) (b) P ( 4 < x < 16 ) (c) P ( x < 9 ) (d) P ( 0 < x < 12 )

To determine

To graph: The probability density function f(x)=3128x over the interval [0,16] and calculate the probabilities (a) P(4<x<9) (b) P(4<x<16), (c) P(x<9),(d) P(0<x<12).

### Explanation of Solution

Given Information:

The probability density function f(x)=3128x over the interval [0,16].

Graph:

Consider the provided probability density function.

f(x)=3128x

Use the ti-83 graphing calculator to construct the graph of the function.

Step 1: Open the ti-83 graphing calculator.

Step 2: Press [Y=] and enter the function Y1=3128x.

Step 3: Press the [WINDOW] key and adjust the scale.

Xmin=0Xmax=16Xscl=1

And,

Ymin=0Ymax=1Yscl=0.1

Step 4: Press the [GRAPH] key.

The graph of the function f(x)=3128x is obtained as,

Now, calculate the probabilities.

Consider the provided probability density function f(x)=3128x.

Use the formula P(cxd)=cdf(x) dx to calculate the required probabilities. So,

P(cxd)=cd3128x dx=3128cd(x)12 dx

Use the formula xndx=xn+1n+1 and integrate.

3128cd(x)12 dx=3128((x)12+112+1)cd=3128(x3/232)cd=3128×23(x3/2)cd=164(x3/2)cd

(a)

To calculate, P(4<x<9), use the Fundamental theorem abf(x) dx=F(b)F(a) and apply the limits on 164(x3/2)cd.

164(x3/2)49=164[(93/2)(43/2)]=164[32×3/222×3/2]=164(3323)=164(278)

Simplify.

164(278)=1964

Thus, the probability of P(4<x<9) is 1964

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Find the 50th derivative of y = cos 2x.

Single Variable Calculus: Early Transcendentals, Volume I

Convert the expressions in Exercises 6584 to power form. xy23

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 89-94, determine whether the statement is true or false. If it is true, explain why it is true. If...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

True or false:

Mathematical Applications for the Management, Life, and Social Sciences

For what values of p does the series converge?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Add the terms in the following expressions. 18y+y

Mathematics For Machine Technology

Distinguish between science and pseudoscience.

Research Methods for the Behavioral Sciences (MindTap Course List)

Describe the similarities and differences between a research proposal and a research report.

Research Methods for the Behavioral Sciences (MindTap Course List) 