Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q.4.13 (page 257)

About 32% of students participate in a community volunteer program outside of school. If 30students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school. Use the TI-83+orTI-84 calculator to find the answer.

Short Answer

Expert verified

The required probability that at most 14students out of 30students selected at random participate in a community volunteer programme outside of school is96.95%or0.9695

Step by step solution

01

Content Introduction

Let the random variable X=number of students participate in community volunteer program outside of school out of30students selected at random.

02

Content Explanation

Assuming that X=0,1,2,.........30

The total number of students is n = 30

The randomly selected students to participate in a community volunteer program outside of school is p =0.32

Now,

q=1-pq=1-0.32q=0.68

Then,Xfollows a binomial distribution

Therefore, the required probability is

P(X≤14)=∑x=014 P(X=x)

Substituting the values we get,

∑x=014 nCxpxqn−x=∑n Cx(0.32)x(0.68)30−x

Upon expanding the summation, we get

30C0(0.32)0(0.68)30−0+30C1(0.32)1(0.68)30−1+30C2(0.32)2(0.68)30−2+……30C14(0.32)14(0.68)30−14

=0.9695=96.5%

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

Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. What values does X take on?

On average, Pierre, an amateur chef, drops three pieces of egg shell into every two cake batters he makes. Suppose

that you buy one of his cakes.

a. In words, define the random variable X.

b. List the values that Xmay take on.

c. Give the distribution ofX.X~_____(_____,_____)

d. On average, how many pieces of egg shell do you expect to be in the cake?

e. What is the probability that there will not be any pieces of egg shell in the cake?

f. Let’s say that you buy one of Pierre’s cakes each week for six weeks. What is the probability that there will not

be any egg shell in any of the cakes?

g. Based upon the average given for Pierre, is it possible for there to be seven pieces of shell in the cake? Why?

A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see if the captains all play the same position. State whether this is binomial or not and state why.

A palette has 200 milk cartons. Of the 200 cartons, it is known that ten of them have leaked and cannot be sold. A stock clerk randomly chooses 18 for inspection. He wants to know the probability that among the 18, no more than two are leaking. Give five reasons why this is a hypergeometric problem.

On average, how many batches should the baker make?

Use the following information to answer the next four exercises: Ellen has music practice three days a week. She practices

for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3%of the time. One

week is selected at random.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

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