At the airport entry sites, a computer is used to randomly decide whether a trav

Question

At the airport entry sites, a computer is used to randomly decide whether a traveler's baggage should be opened for inspection. If the chance of being selected is 12%. There are 50 baggage items waiting to be loaded.

*What is the probability that exactly 8 out of the 50 items will be opened?

*What is the probability that at least 8 out of the 50 items will be opened?

*What is the probability that 8 or fewer out of the 50 items will be opened?

*How many are expected to be open?

*Would that be unusual if a. ALL 50 items will be opened? b. NONE 50 items will be opened? c. 3 of 50 items will be opened? d. 25 of 50 items will be opened?

Explanation / Answer

X = number of luggage wgr will be opened

X follow binomial distribution with n = 50 , p =0.12

a)

P(X = 8) = 0.10754

b)P(X >=8) = 0.246747

c)

P(X <= 8) = 0.860799

d) E(X) = np = 50* 0.12 = 6

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