Chapter 7, Problem 19P

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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

Explanation

**Given info:**

The random variable *X* denote the scores follow normal distribution with a mean of

**Calculation:**

*z-score:*

Where,

Substitute the values in the above formula is as follows:

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

**(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

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