   Chapter 7, Problem 16P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A population of scores forms a normal distribution with a mean of μ = 80 and a standard deviation of σ = 10. a. What proportion of the scores have values between 75 and 85? b. For samples of n = 4, what proportion of the samples will have means between 75 and 85? c. For samples of n = 16, what proportion of the samples will have means between 75 and 85?

(a)

To determine

To find: The proportion of scores has values between 75 and 85.

Explanation

Given info:

The random variable X denote the scores follow normal distribution with a mean of μ=80 and standard deviation of σ=10.

Calculation:

z-score:

z=Xμσ

Substitute the values in the above formula is as follows:

z1=758010=0.50

z2=858010=0.50

The probability of specified z-values using the Excel formula:

P(75<X<85)=P(0.50<z<0.50)=P(z<0

(b)

To determine

To find: The proportion of samples will have means between 75 and 85.

(c)

To determine

To find: The proportion of samples will have means between 75 and 85.

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