   Chapter 9.2, Problem 24E ### 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 ) = 5 4 ( x + 1 ) 2 , [ 0 , 4 ] (a) P ( 0 < x < 2 ) (b) P ( 2 < x < 4 ) (c) P ( 1 < x < 3 ) (d) P ( x ≤ 2 )

(a)

To determine

The probability P(0<x<2), for the probability density function f(x)=54(x+1)2 over the interval [0,4]

Explanation

Given Information:

The function, f(x)=54(x+1)2 is a probability density function over the interval [0,4].

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)=54(x+1)2

The function is a probability density function over the interval [0,4].

Therefore, f(x) is continuous and non-negative over the interval [0,4] 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=5/4(x+1)2.

Step4: Press Enter button.

Step5: Press Window and set is as:

Xmin=0.5;            Xmax=3;                Xscal=1Ymin=0.5;            Ymax=0.5;             Yscal=1

Step6: Press Graph button.

(b)

To determine

The probability P(2<x<4), for the probability density function f(x)=54(x+1)2 over the interval [0,4].

(c)

To determine

The probability P(1<x<3), for the probability density function f(x)=54(x+1)2 over the interval [0,4].

(d)

To determine

The probability P(x3), for the probability density function f(x)=54(x+1)2 over the interval [0,4].

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