Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q5CQQ (page 226)

Notation

a. Identify the values of \(\mu \) and \(\sigma \) for the standard normal distribution.

b. What do the symbols \({\mu _{\bar x}}\) and \({\sigma _{\bar x}}\)represent?

Short Answer

Expert verified
  1. The symbols\(\mu \;{\rm{and}}\;\sigma \) represent the mean and standard deviation of population values respectively. Thus, \(\mu = 0,\;{\rm{and}}\;\sigma = 1\) for standard normal distribution.
  1. The symbols\({\mu _{\bar x}},{\sigma _{\bar x}}\)represent the mean and standard deviation of all the sample mean values of a specific sample size respectively.

Step by step solution

01

Given information

Certain notations are mentioned.

02

Describe the random variablefor population

a.

Let X be the random variable for population of all observations, which follows standard normal distribution.

The mean of the population is represented by \(\mu \). For standard normal distribution, mean is known to be 0.

The standard deviation of the population is represented by \(\sigma \). For standard normal distribution, standard deviation is known to be 1.

Thus, \(X \sim N\left( {\mu = 0,\sigma = 1} \right)\).

03

Describe the random variable for samples

b.

Let \(\bar X\) be the random variable for sample means of different equally sized samples taken from population.

The mean of the sample mean distribution is \({\mu _{\bar x}}\).

The standard deviation of sample mean distribution is \({\sigma _{\bar x}}\) .

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Standard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -2.00 and 2.00.

In Exercises 11–14, use the population of {34, 36, 41, 51} of the amounts of caffeine (mg/12oz) in Coca-Cola Zero, Diet Pepsi, Dr Pepper, and Mellow Yello Zero.

Assume that  random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Range Repeat Exercise 11 using ranges instead of means.

In Exercises 21–24, use these parameters (based on Data Set 1 “Body Data” in Appendix B):• Men’s heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in.• Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.Mickey Mouse Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as Mickey Mouse characters?

b. If the height requirements are changed to exclude the tallest 50% of men and the shortest 5% of men, what are the new height requirements?

Standard normal distribution, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, Draw a graph, then find the probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.

Less than 0

Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45–48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.

About______ % of the area is between z = -2 and z = 2 (or within 2 standard deviation of the mean).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free