/*! 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} Q.AP2.25 - Cumulative AP Practise Test 聽In a city library, the mean nu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q.AP2.25 - Cumulative AP Practise Test (page 438)

In a city library, the mean number of pages in a novel is 525 with a standard deviation of 200. Approximately 30%of the novels have fewer than 400 pages. Suppose that you randomly select 50 novels from the library.

a. What is the probability that the average number of pages in the sample is less than 500 ?

b. What is the probability that at least 20 of the novels have fewer than 400 pages?

Short Answer

Expert verified

(a)the probability that the total number of pages is less than 25,000 is 0.1894

(b)Then approximation the binomial distribution by the normal distribution渭p^=p=0.30

Step by step solution

01

Part (a) Step 1: Given Information

渭=525蟽=200n=50

Formula used:

z=x炉-渭蟽/n

02

Part (a) Step 2: Simplification

Sample mean is

25,0050=500z=x炉-渭蟽/n=500-525200/50=-0.88P(x炉<500)=P(Z<-0.88)=0.1894

Therefore the probability that the total number of pages is less than 25,000 is 0.1894

03

Part (b) Step 1: Given Information

n=50p=30%=0.30

Formula used:

蟽p^=p(1-p)nz=x-渭蟽

04

Part (b) Step 2: Simplification

For a normal approximation of the binomial distribution: np鈮�and nq鈮�10.

np=50(0.30)=15鈮�10nq=n(1-p)=50(1-0.35)=35鈮�10

Then approximation the binomial distribution by the normal distribution

渭p^=p=0.30

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

Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "Go ahead." Customs agents claim that 30%of all travelers will be stopped (red light), because the light has probability of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100 travelers push the button. Only 20 get a red light.

a. Assume that the customs agents' claim is true. Find the probability that the proportion of travelers who get a red light in a random sample of 100 travelers is less than or equal to the result in this sample.

b. Based on your results in part (a), is there convincing evidence that less than 30%of all travelers will be stopped? Explain your reasoning.

Doing homework A school newspaper article claims that 60%of the students at a large high school completed their assigned homework last week. Assume that this claim is true for the 2000students at the school.

a. Make a bar graph of the population distribution.

b. Imagine one possible SRS of size 100from this population. Sketch a bar graph of the distribution of sample data.

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is and the standard deviation of the loss is 蟽=\(5000.The distribution of losses is strongly right-skewed: many policies have \)0loss, but a few have large losses. The company hopes to sell 1000 of these policies for \(300each.

a. Assuming that the company鈥檚 claim is true, what is the probability that the mean loss from fire is greater than \)300for an SRS of 1000 homeowners?

b. If the company wants to be 90% certain that the mean loss from fire in an SRS of 1000 homeowners is less than the amount it charges for the policy, how much should the company charge?

A sample of teens A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13to 16year-olds. The researchers will report the mean xfrom their sample as an estimate of the mean cholesterol level 渭in this population. Explain to someone who knows little about statistics what it means to say that xis an unbiased estimator of 渭.

Songs on an iPod Refer to Exercise 53 . How many songs would you need to sample if you wanted the standard deviation of the sampling distribution ofx-x炉 to be 10 seconds? Justify your answer.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.