Chapter 7, Problem 17P

### 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

# For random samples of size n = 25 selected from a normal distribution with a mean of μ = 50 and a standard deviation of σ = 20, find each of the following: a. The range of sample means that defines the middle 95% of the distribution of sample means. b. The range of sample means that defines the middle 99% of the distribution of sample means.

a.

To determine
The range of sample means that defines the middle 95% of the distribution of sample means.

Explanation

Given info:

Sample size is given as n=25.

Population mean is μ=50.

Population standard deviation is σ=20.

Confidence interval is given as 95%.

Calculation:

The symbols μ and σ represent the population mean and standard deviation respectively. Let M represents sample mean. Then for calculating the range need to find standard error:

σM=σn=2025=205=4

Now the z score value for middle 95% or for two tailed with alpha level 0.05 using z table is ±1.96. Now for calculating range of sample means:

μ=M±z(se)

Where, z is for z score and se for standard error

b.

To determine
The range of sample means that defines the middle 99% of the distribution of sample means.

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