   # 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 ) = 1 16 , [ 0 , 16 ] (a) P ( 0 &lt; x &lt; 6 ) (b) P ( 12 &lt; x &lt; 13 ) (c) P ( x ≥ 5 ) (d) P ( 8 &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 31RE
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 ) = 1 16 , [ 0 , 16 ] (a) P ( 0 < x < 6 ) (b) P ( 12 < x < 13 ) (c) P ( x ≥ 5 ) (d) P ( 8 < x < 12 )

To determine

To graph: The probability density function f(x)=116 over the interval [0,16] and calculate the probabilities (a) P(0<x<6)(b) P(12<x<13), (c) P(x5),(d) P(8<x<12).

### Explanation of Solution

Given Information:

The probability density function f(x)=116 over the interval [0,16].

Graph:

Consider the provided probability density function.

f(x)=116

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=116.

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

Xmin=0Xmax=18Xscl=1

And

Ymin=0Ymax=216Yscl=0.01

Step 4: Press the [GRAPH] key.

The graph of the function f(x)=116 is obtained as,

Now, calculate the probabilities.

Consider the provided probability density function f(x)=116.

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

P(cxd)=cd116 dx

Use the formula cdx=cx and integrate.

cd116 dx=116(x)cd

(a)

To calculate P(0<x<6), use the Fundamental theorem abf(x) dx=F(b)F(a) and apply the limits on 116(x)cd.

116(x)06=116(60)=616=38

Thus, the probability of P(0<x<6) is 38

### 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
Investments In Hedge Funds Investments in hedge funds have increased along with their popularity. The assets of...

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

In problems 23-58, perform the indicated operations and simplify. (x4+3x3x+1)(x2+1)

Mathematical Applications for the Management, Life, and Social Sciences

Differentiate. y=ex1ex

Single Variable Calculus: Early Transcendentals

Arc Length Give the integral formula for arc length inparametric form.

Calculus: Early Transcendental Functions (MindTap Course List)

What degree Taylor polynomial about a = 1 is needed to approximate e1.05 accurate to within 0.0001? n = 2 n = 3...

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

Given that for all x, a power series for is:

Study Guide for Stewart's Multivariable Calculus, 8th 