Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q.9 (page 460)

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is 16.05ounces with a standard deviation of 0.1ounces. Assume that the machine is working properly. If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95%of the observations should occur in which interval?

(a) 16.05to 16.15ounces

(b) 0.30to 0.30ounces

(c) 15.95to16.15 ounces

(d) 15.90to 16.20ounces

(e) None of the above

Short Answer

Expert verified

The correct answer is (e)

Step by step solution

01

Given Information

Amount of bottles of shampoo to fill the machıne =16ounces

Mean amount of shampoo =16.05ounces

Standard deviation =0.1ounce

Number of randomly selected bottles=4

02

Explanation

Consider that nrepresents the number of randomly selected bottles that is, n=4;σrepresents the standard deviation that is σ=0.1, and μdenotes the mean that is, μ=16.05.

In the case of a Normal distribution, it is known that 95%the observations lie within 2standard deviations of the mean. But it is not given that the population distribution is normal so the central limit theorem cannot be applied.

Hence, the correct answer is (e).

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

Here is a dot plot of the adult literacy rates in 177countries in 2008, according to the United Nations. For example, the lowest literacy rate was 23.6%, in the African country of Burkina Faso. Use the dot plot below to answer Questions

Based on the shape of this distribution, what numerical measures would best describe it?

(a) The five-number summary

(b) The mean and standard deviation

(c) The mean and the quartiles

(d) The median and the standard deviation

(e) It is not possible to determine which numerical values to use.

The probability distribution for the number of heads in four tosses of a coin is given by

Number of heads01234
Probability0.0625
0.2500
0.3750
0.2500
0.0625

The probability of getting at least one tail in four tosses of a coin is

(a) 0.2500. (b)0.3125(c) 0.6875(d)0.9375 (d) None of these

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500people to about 4000people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

(a) reduce the bias of the estimate.

(b) increase the bias of the estimate.

(c) reduce the variability of the estimate.

(d) increase the variability of the estimate.

(e) have no effect since the population size is the same

About 75%of young adult Internet users (ages 18 to 29) watch online video. Suppose that a sample survey contacts an SRS of 1000 young adult Internet users and calculates the proportion p^in this sample who watch online video.

4. If the sample size were 9000 rather than 1000 , how would this change the sampling distribution of p^?

(a) Sketch a possible graph of the distribution of sample data for an SRS of size 5 with a range of 1000grams.

(b) Explain why the dotplot of sample ranges above is not the actual sampling distribution of the sample range.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

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.

Sign-up for free