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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 ofX.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. number of students who attend the Tet festivities

b. 0,1,2,3,4,5,6,7,8,9,10,11,12

c. X~Binom⁡(n=12,p=0.18)

d. E(X)=np=12∗0.18=2.16

e. probability that at most four students will attend =0.9511

f. Probability that more than two students will attend=0.3702

Step by step solution

01

Given information

Total number of students surveyed 12

probability of students attended Tet festive 0.18

02

Explanation (part a)

Xthe random variable of interest "number of students who attend the Tet festivities".

03

Explanation (part b)

The possible values for the random variableX
are :0,1,2,3,4,5,6,7,8,9,10,11,12

04

Explanation (part c)

The distribution for Xon this case is given by:

X~Binom⁡(n=12,p=0.18)

05

Explanation (part d)

The number of students expected to join in 12random variables of 18%of students is given by,

E(X)=np=12∗0.18=2.16

06

Explanation (part e)

the probability that at most four students will attend:

P(X≤4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)=0.9511

07

Explanation (part f)

the probability that more than two students will attend:

P(X>2)=1−P(X≤2)=1−[P(X=0)+P(X=1)+P(x=2)]=1−[0.09242+0.24345+0.29392]=0.3702

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