Question

An airline estimates that 94% of people booked on their flights actually show up. The airline booked 73 people for a flight to Hawaii. Let X = the number of people that actually show up for the flight to Hawaii out of 73 bookings. a. [2 pts] What is the probability that exactly 73 people actually show up? b. [2 pts] What is the probability that at most 65 people actually show up? c. [2 pts] What is the probability that at least 70 people actually show up? (Submit a copy of the Graph from StatCrunch that shows this probability.) d. [3 pts] What are the mean and standard deviation for the number of people that actually show up? e. [3 pts] Would 73 people actually showing up be considered a significantly high number of people?

Answer 1

This becomes a case of binomial distribution with p = 0.94 and n = 73.

We know that,

P(X=x) = (nCx)*p^x(1-p)^n-x

A.

P(X=73) = 0.01092

B.

P(X65) = 0.0708

C.

P(X70) = 0.35544

D.

Mean = n*p

= 73*0.94

= 68.62

Std. Deviation =

= 2.029

E.

P(X=73) = 0.01092 < 0.05 i.e. it is a significantly higher number.

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