Chapter 7, Problem 17P

BuyFind*arrow_forward*

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

Population mean is

Population standard deviation is

Confidence interval is given as 95%.

**Calculation:**

The symbols
*M* represents sample mean. Then for calculating the range need to find standard error:

Now the z score value for middle 95% or for two tailed with alpha level 0.05 using z table is

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.

Probability and Statistics for Engineering and the Sciences

Essentials Of Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Understanding Basic Statistics

Calculus: Early Transcendentals

Single Variable Calculus: Early Transcendentals

Multivariable Calculus

Finite Mathematics for the Managerial, Life, and Social Sciences

Contemporary Mathematics for Business & Consumers

Mathematical Applications for the Management, Life, and Social Sciences

Intermediate Algebra

Finite Mathematics

Calculus of a Single Variable

Elementary Geometry For College Students, 7e

Single Variable Calculus: Early Transcendentals, Volume I

Precalculus: Mathematics for Calculus (Standalone Book)

Elementary Technical Mathematics

Single Variable Calculus

Calculus: An Applied Approach (MindTap Course List)

Elements Of Modern Algebra

Trigonometry (MindTap Course List)

Calculus (MindTap Course List)

Calculus: Early Transcendental Functions (MindTap Course List)

Applied Calculus

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Calculus (MindTap Course List)

Mathematical Excursions (MindTap Course List)

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus: Early Transcendental Functions

Introduction To Statistics And Data Analysis

Elementary Geometry for College Students

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th