   Chapter 9.2, Problem 20E ### 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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# Finding a Probability In Exercises 19-26, sketch the graph of the probability density function over the indicated interval and find each probability. See Example 3. f ( x ) = 1 7 , [ 0 , 7 ] (a) P ( 0 < x < 5 ) (b) P ( 4 < x < 5 ) (c) P ( 3 < x < 7 ) (d) P ( x = 6 )

(a)

To determine

The probability P(0<x<5), for the probability density function f(x)=17 over the interval [0,7].

Explanation

Given Information: The function, f(x)=17 is a probability density function over the interval [0,7]

Formula used:

Consider a function f of a continuous random variables x whose set of values is the interval [a,b], A function is a probability density function when it is non-negative and continuous on the interval [a,b] and when abf(x)dx=1 and the probability P(a<x<b)=abf(x)dx.

Calculation:

Consider the function,

f(x)=17

The function is a probability density function over the interval [0,7].

Therefore, f(x) is continuous and non-negative over the interval [0,7] and is graphed as shown below:

Now use Ti-83 graphing calculator to draw the graph:

Step1: Open Ti-83.

Step2: Press Y= button.

Step3: Write the equation as Y1=1/7.

Step4: Press Enter button.

Step5: Press Window and set is as:

Xmin=0.5;            Xmax=3;                Xscal=1Ymin=0

(b)

To determine

The probability P(4<x<5), for the probability density function f(x)=17 over the interval [0,7],

(c)

To determine

The probability P(3<x<7), for the probability density function f(x)=17 over the interval [0,7].

(d)

To determine

The probability P(x=6), for the probability density function f(x)=17 over the interval [0,7].

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