A school newspaper reporter decides to randomly survey 11 students to see if the

Question

A school newspaper reporter decides to randomly survey 11 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 17% 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.

Part (c)

Give the distribution of X.
X ~ B (     ,      )

Part (d)

How many of the 11 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

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.)

Explanation / Answer

a) X = number of students who will attend the festivities

c) X ~ B ( 0.17 , 11)

d) Expected students to attend the festivities = n * p = 11 * 0.17 = 1.87 = 2

e) P(X = x) = 11Cx * 0.17x * (1 - 0.17)11-x

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

              = 11C0 * 0.170 * 0.8311 + 11C1 * 0.171 * 0.8310 + 11C2 * 0.172 * 0.839 + 11C3 * 0.173 * 0.838

              = 0.8987

f) P(X > 2) = 1 - P(X < 2)

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

                 = 1 - [11C0 * 0.170 * 0.8311 + 11C1 * 0.171 * 0.8310 + 11C2 * 0.172 * 0.839 ]

                 = 1 - 0.7161

                 = 0.2839

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