Chapter 7, Problem 13P

### Essentials of Statistics for the B...

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

Chapter
Section

### Essentials of Statistics for the B...

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

# The population of IQ scores forms a normal distribution with a mean of μ = 100 and a standard deviation of σ = 15. What is the probability of obtaining a sample mean greater than M = 97. a. for a random sample of n = 9 people? b. for a random sample of n = 25 people?

a.

To determine

To dtermine: The probability of obtaining a sample mean greater than M=97 for given sample.

Explanation

Given info:

Numbers of people in a random sample are n=9 with population mean is μ=100 and  population standard deviation is σ=15 with sample mean is M=97.

Calculation:

If μ and σ represents the population mean and standard deviation respectively. Let n represents numbers of scores in each sample. Let M represents given sample mean. Then,

μ=100σ=15n=9M=97

Let X¯ represents the random sample mean from given distribution. Let μM and σM represents mean and standard error of X¯ Then, expected mean of X¯ will be same as population mean and standard error is calculated as:

μM=100σM=159=153=5

Let p represents the probability that random mean is greater than M=97

b.

To determine
The probability of obtaining a sample mean greater than M=97 for given sample.

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