   Chapter 7, Problem 19P 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

At the end of the spring semester, the Dean of Students sent a survey to the entire freshman class. One question asked the students how much weight they had gained or lost since the beginning of the school year. The average was a gain of μ. = 9 pounds with a standard deviation of σ = 6. The distribution of scores was approximately normal. A sample of n = 4 students is selected and the average weight change is computed for the sample. a. What is the probability that the sample mean will be greater than M = 10 pounds? In symbols, what is p(M > 10)? b. Of all of the possible samples, what proportion will show an average weight loss? In symbols, what is p(M < 0)? c. What is the probability that the sample mean will be a gain of between M = 9 and M = 12 pounds? In symbols, what is p(9 < M < 12)?

(a)

To determine

To find: The probability that the sample mean will be greater than M=10 pounds.

Explanation

Given info:

The random variable X denote the scores follow normal distribution with a mean of μ=9 and standard deviation of σ=6. The sample mean is M=10 and the sample size is n=4.

Calculation:

z-score:

z=MμσM

Where, σM=σn

Substitute the values in the above formula is as follows:

z=10964=0.33

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

P(M>10)=P(z>0

(b)

To determine

To find: The proportion which will show an average weight loss.

(c)

To determine

To find: The probability that the sample mean will be a gain of between M=9 and M=12.

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