Question

An article reported that what airline passengers like to do most on long flights is rest or sleep; in a survey of 3697 passengers, almost 80% did so. Suppose that for a particular route the actual percentage is exactly 80%, and consider randomly selecting nine passengers. Then x, the number among the selected nine who rested or slept, is a binomial random variable with n = 9 and p = 0.8. (Round your answers to four decimal places.)

(a) Calculate p(6).

b) Calculate p(9), the probability that all nine selected passengers rested or slept.
p(9) =  

(c) Determine P(x ≥ 6).

Answer 1

Solution :

X is binomial distributed random variable with parameter n = 9 and p = 0.8.

According to binomial probability law probability of occurrence of exactly x success in n trials is given by,

Where, p is probability of success.

a) We have to obtain P(X = 6).

We have, p = 0.8 and n = 9

Using binomial probability law we get,

Hence, P(6) = 0.1762

b) We have to obtain P(X = 9).

We have, p = 0.8 and n = 9

Using binomial probability law we get,

Hence, P(9) = 0.1342

c) We have to obtain P(x ≥ 6).

Using binomial probability law we get,

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