   # Education In 2013, the scores on the Medical College Admission Test (MCAT) can be modeled by a normal probability density function with a mean of 25.3 and a standard deviation of 6.5. (Source: Association of American Medical Colleges) (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 MCAT scored between 20 and 35. (c) Use a symbolic integration utility to approximate the probability that a person who took the MCAT scored more than 36. ### 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 61RE
Textbook Problem
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## Education In 2013, the scores on the Medical College Admission Test (MCAT) can be modeled by a normal probability density function with a mean of 25.3 and a standard deviation of 6.5. (Source: Association of American Medical Colleges)(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 MCAT scored between 20 and 35.(c) Use a symbolic integration utility to approximate the probability that a person who took the MCAT scored more than 36.

(a)

To determine

To graph: The sketch of distribution of the scores in MCAT using graphing utility where the scores are normally distributed with a mean and standard deviation of 25.3 and 6.5 respectively.

### Explanation of Solution

Given Information:

The scores are normally distributed with a mean and standard deviation of 25.3 and 6.5 respectively.

Graph:

The normal probability density function is given by

f(x)=1σ2πe(xμ)2(2σ2),<x<

Substitute μ=25.3 and σ=6.5 in the above equation,

f(x)=16.52πe(x25.3)22(6.5)2=0.0614e(x25.3)284

(b)

To determine

To calculate: The approximate probability that the score of the person who took MCAT is between 20 and 35 using symbolic integration utility.

(c)

To determine

To calculate: The approximate probability that the MCAT score of the person is more than 36 using symbolic integration utility.

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