/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 A population has a normal distri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 22

A population has a normal distribution. A sample of size \(n\) is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases. a. \(n=94\) b. \(n=11\)

Short Answer

Expert verified
For \(n=94\), the sampling distribution of the sample mean will be approximately normal due to the Central Limit Theorem. For \(n=11\), the shape might not be normal because it's not a large enough sample size to assure normality via the Central Limit Theorem, unless the population itself is normally distributed.

Step by step solution

01

Shape of the Sampling Distribution for case a

Given that \(n=94\) which is larger than 30, the sampling distribution of the mean will be approximately normal. The Central Limit theorem assures this.
02

Shape of the Sampling Distribution for case b

In the case of \(n=11\), which is less than 30, we cannot ensure the normality of the sampling distribution of the mean. Although Central Limit theorem works for smaller samples as well, as a rule of thumb, it is commonly used when \(n>30\). If the population from which this sample of 11 observations is drawn is not normal, then the shape can differ significantly from a normal distribution.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

According to the American Time Use Survey results released by the Bureau of Labor Statistics on June 24,2015, on a typical day, \(65 \%\) of American men age 15 and over spent some time doing household activities such as housework, cooking, lawn care, or financial and other household management. Assume that this percentage is true for the current population of all American men age 15 and over. A random sample of 600 American men age 15 and over is selected. a. Find the probability that the sample proportion is \(\begin{array}{ll}\text { i. less than .68 } & \text { ii. between } .63 \text { and } .69\end{array}\) b. What is the probability that the sample proportion is within \(.025\) of the population proportion? c. What is the probability that the sample proportion is greater than the population proportion by \(.03\) or more?

What is the estimator of the population proportion? Is this estimator an unbiased estimator of \(p ?\) Explain why or why not.

A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population of all people who ride this elevator have a mean weight of 160 pounds with a standard deviation of 25 pounds. If 35 of these people board the elevator, what is the probability that their combined weight will exceed 6000 pounds? Assume that the 35 people constitute a random sample from the population.

A television reporter is covering the election for mayor of a large city and will conduct an exit poll (interviews with voters immediately after they vote) to make an early prediction of the outcome. Assume that the eventual winner of the election will get \(60 \%\) of the votes. a. What is the probability that a prediction based on an exit poll of a random sample of 25 voters will be correct? In other words, what is the probability that 13 or more of the 25 voters in the sample will have voted for the eventual winner? b. How large a sample would the reporter have to take so that the probability of correctly predicting the outcome would be \(.95\) or higher?

Let \(\bar{x}\) be the mean of a sample selected from a population. a. What is the mean of the sampling distribution of \(\bar{x}\) equal to? b. What is the standard deviation of the sampling distribution of \(\bar{x}\) equal to? Assume \(n / N \leq .05\).
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.