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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鈮�14)=鈭�x=014鈥�P(X=x)

Substituting the values we get,

鈭�x=014鈥�nCxpxqn鈭�x=鈭�n鈥�Cx(0.32)x(0.68)30鈭�x

Upon expanding the summation, we get

30C0(0.32)0(0.68)30鈭�0+30C1(0.32)1(0.68)30鈭�1+30C2(0.32)2(0.68)30鈭�2+鈥�鈥�30C14(0.32)14(0.68)30鈭�14

=0.9695=96.5%

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