   # Education For high school graduates from 2012 through 2014, the scores on the ACT Test can be modeled by a normal probability density function with a mean of 21.0 and a standard deviation of 5.4. (Source: ACT, Inc.) (a) Use a graphing utility to graph the distribution. (b) Use a symbolic integration utility to approximate the probability that a person who took the ACT scored between 24 and 36. (c) Use a symbolic integration utility to approximate the probability that a person who took the ACT scored more than 26. ### 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 9.3, Problem 56E
Textbook Problem
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## Education For high school graduates from 2012 through 2014, the scores on the ACT Test can be modeled by a normal probability density function with a mean of 21.0 and a standard deviation of 5.4. (Source: ACT, Inc.)(a) Use a graphing utility to graph the distribution.(b) Use a symbolic integration utility to approximate the probability that a person who took the ACT scored between 24 and 36.(c) Use a symbolic integration utility to approximate the probability that a person who took the ACT scored more than 26.

(a)

To determine

To graph: The provided normal probability density function by the use of a graphing utility if the score on ACT test of high school graduates from 2012 to 2014 is modelled by a normal probability density function.

### Explanation of Solution

Given information:

For the normal probability density function the mean is μ=21 and standard deviation is σ=5.4

Graph:

The normal probability density function is given by

f(x)=1σ2πe(xμ)2(2σ2),<x<

Substitute μ=21 and σ=5.4 in the above equation,

f(x)=15.42πe(x21)22(5.4)2=0.0738e(x21)258

(b)

To determine

To calculate: The approximate probability that when a person took ACT, scores between 26 to 36 by the use of symbolic integration utility.

(c)

To determine

To calculate: The approximate probability of that when a person took ACT, scores more than 26 by the use of symbolic integration utility.

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