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Chapter 4: Q. 88 (page 293)

A school newspaper reporter decides to randomly survey 12students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18%of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

a. In words, define the random variable X.

b. List the values that Xmay take on.

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

d. How many of the 12students do we expect to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend

Short Answer

Expert verified

(a) The random variable Xis the number of students who will attend the festivities

(b) The values of Xare 0,1,2,3,4,5,6,7,8,9,10,11,12

(c) the distribution of Xis X~B(12,0.18)

(d) The expected value of 12students attending the festivities is 2.16

(e) The probability of most four students attending the test is 0.95107

(f) The probability of more than two students attending the test is 0.37021

Step by step solution

01

The variable X and the values (part a and b)

The variable Xrepresents the number of students attending the exam

The values Xare 0,1,2,3,4,5,6,7,8,9,10,11,12

02

Distribution of X (part c)

With 12trials and a probability of success of 0.18, variable Xhas a binomial distribution.

X~B(12,0.18)

03

The expected value of 12 students to attend the festivities (part d)

渭=n脳pis the estimate of a binomial distribution. Since n=12and p=0.18, variable Xexpected value is

=12脳0.18=2.16

04

The probability of most four students attend the test  (part e)

There's a good chance that at least four pupils will show up for the test is 0.95107

Standard deviation is given by, 蟽=鈭�xi鈭�渭2N

Plugging all the values we get,

localid="1651755910621" 蟽=12脳0.18(1-0.18)=1.331

Also, Variance = 蟽2

Hence variance =localid="1651848556316" role="math" 蟽2=1.771

05

The probability of more than two students attend the test (part f)

There's a chance that more than two students will show up for the test is0.37021

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