Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q. 69 (page 481)

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the histogram of the sample values looks more and more Normal." Is the student right? Explain your answer.

Short Answer

Expert verified

The statement explained by the student is wrong, because the histogram of sample values becomes more Normal as you take larger and larger samples from a population.

Step by step solution

01

Given information

The student made a statement "The histogram of the sample values looks more and more Normal when you take larger and larger samples from a population."

02

According to Question 

It's incorrect because as the sample size grows, the histogram of sample values will take on the shape of the population 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.

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

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

At a traveling carnival, a popular game is called the “Cash Grab.” In this game, participants step into a sealed booth, a powerful fan turns on, and dollar bills are dropped from the ceiling. A customer has 30 seconds to grab as much cash as possible while the dollar bills swirl around. Over time, the operators of the game have determined that the mean amount grabbed is \(13 with a standard deviation of \)9. They charge \(15 to play the game and expect to have 40 customers at their next carnival.

a. What is the probability that an SRS of 40 customers grab an average of \)15 or more?

b. How much should the operators charge if they want to be 95% certain that the mean amount grabbed by an SRS of 40 customers is less than what they charge to play the game?

Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. A commuter plane carries 30 passengers. Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft2 ) and a standard deviation of 2 ft2 . To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to bex=249.6ft2.

a. Find the probability that the sample mean area is 249.6ft2or less if the manufacturer’s claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average area of its aluminum foil rolls?

Even more tall girls, Refer to Exercises 12and 14. Suppose that the sample mean height of the twenty 16-year-old females is x=65.8inches. Would this sample mean provide convincing evidence that the average height of all 16-year-old females at this school is greater than 64inches? Explain your reasoning.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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