Question

A school newspaper reporter decides to randomly survey 20 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

• In words, define the Random Variable X.

• Part (b)

  List the values that X may take on.

  X = 0, 1, 2, ..., 23 X = 1, 2, 3, ..., 20  X = 1, 2, 3, ..., 23 X = 0, 1, 2, ..., 20

• Part (c)

  Give the distribution of X.
  X ~  

• Part (d)

  How many of the 20 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 6 students will attend. (Round your answer to four decimal places.)

• Part (f)

  Find the probability that more than 4 students will attend. (Round your answer to four decimal places

Answer 1

(a)

The Random Variable X. is defined as follows:

X = the number of students who will attend the festivities

(b)

Correct option:

X = 0, 1, 2, ..., 20

(c)

X Bin (20, 0.23).

The random variableX has binomial distribution with parameters n = 20 and p = 0.23

(d)

Number of students we expect to attend the festivities = = np = 20 X 0.23 = 4.6 = 5 (Round to integer)

(e)
P(X6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

So,

P(X6) = 0.8443

So,

Answer is:

0.8443

(f)

P(X>4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]

So,

P(X>4) = 1 - 0.4986

        = 0.5014

So,

Answer is:

0.5014