   # An intelligence quotient or IQ is a number that is meant to measure intelligence. The IQs of students in a school are normally distributed with a mean of 110 and a standard deviation of 10. Use a symbolic integration utility to approximate the probability that a student at the school will have an IQ (a) within one standard deviation of the mean and (b) greater than 130. ### 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 16TYS
Textbook Problem
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## An intelligence quotient or IQ is a number that is meant to measure intelligence. The IQs of students in a school are normally distributed with a mean of 110 and a standard deviation of 10. Use a symbolic integration utility to approximate the probability that a student at the school will have an IQ (a) within one standard deviation of the mean and (b) greater than 130.

(a)

To determine

To calculate: The approximate probability that a student at school will have an IQ within one standard deviation of the mean using symbolic integration utility where IQ is a number used to measure intelligence of students in a school and it is normally distributed with a mean and standard deviation of 110 and 10 respectively.

### Explanation of Solution

Given Information:

The intelligence of students in a school is normally distributed with a mean and standard deviation of 110 and 10 respectively.

Formula used:

If f is any probability density function of any random variable x on the interval [a,b], then the probability of x is given as,

P(axb)=abf(x)dx

Calculation:

The normal probability density function is given by

f(x)=1σ2πe(xμ)2(2σ2),<x<

Substitute μ=110 and σ=10 in the above equation,

f(x)=1102πe(x110)22(10)2=0

(b)

To determine

To calculate: The approximate probability that a student at school will have an IQ greater than 130 using symbolic integration utility.

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