Question

A school newspaper reporter decides to randomly survey 16 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 12% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

• Part (a)

  In words, define the Random Variable X.

  the types of festivities offered at the schoolthe number of students in the school    the school newspaperthe number of students that will attend Tet

• Part (b)

  List the values that X may take on.

  X = 1, 2, 3, ..., 16X = 0, 1, 2, ..., 12    X = 0, 1, 2, ..., 16X = 1, 2, 3, ..., 12

• Part (c)

  Give the distribution of X.
  X ~     ,  

• Part (d)

  How many of the 16 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)
  student(s)

• Part (e)

  Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

• Part (f)

  Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

Answer 1

a) X will be defined as : no of students that will attend tet.

b) Kis of values X may take :

X= 0,1,2,3,......16.

c) Distribution of X:

X follows binomial distribution with parameters n ( no of trials) and p (probability of success in none trial)

Where n= 16 and p= 0.12.

X~binomial(n=16,p=.12)

d) Expectation of X is given as n*p

So total no of expected students attending get = 16* .12 = 2

E) P(X<=3)= P(X=0)+P(X=1)+P(X=2)+P(X=3)

= 0.8837

Where P(X=X) is given by binomial formula

n​​​​​​C​​​​x​*(p)x​(1-p)n-x

putting n=16,p=.12 and X=0,1,2and 3 we get probabilities in above equation. By summing them we obtain desired result as 0.8837.

F) P( X>2)= 1-P(X<=2)=1-[P(X=0)+P(X=1)+P(X=2)]

=1-0.7001=0.2998