   Chapter 8.4, Problem 36E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Testing The Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school are normally distributed, with a mean of 500 and a standard deviation of 100. What is the probability that an individual chosen at random has a score(a) greater than 700? (b) less than 300?(c) between 550 and 600?

(a)

To determine

To calculate: The probability that individual chosen at random has a score greater than 700 using standard normal distribution if the mean of Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school is 500, and a standard deviation of 100.

Explanation

Given Information:

A score greater than 700, so the probability is Pr(x>700).

The mean is 500, and a standard deviation of 100.

Formula used:

If data for a population are normally distributed, the z score is,

z=xμσ

Where σ is the standard deviation of the population data, x is the number of standard deviation and μ is mean.

Calculation:

Consider the provided probability Pr(x>700),

The mean is μ=500 and the standard deviation σ=100.

To find the value of provided probability use the formula z=xμσ.

So this will convert into:

Pr(xμσ>700500100)=Pr(z>200100)=Pr(z>2)

As normal distribution is symmetric about mean 0

(b)

To determine

To calculate: The probability that individual chosen at random has a score less than 300 using standard normal distribution if the Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school if the mean is 500, and a standard deviation of 100.

(c)

To determine

To calculate: The probability that individual chosen at random has a score between 550 and 600 using standard normal distribution if the Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school if the mean is 500, and a standard deviation of 100.

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