Question

An airline estimates that 94% of people booked on their flights actually show up. if the airline books 54 people for a flight, what is the probability that 50 or more people will show up for the flight (round 4 decimals)

Answer 1

An airline estimates that 94% of people booked on their flights actually show up.

Airline books 54 people

Let X be the number of people who will show up out of these 54 people

So, let X follows Binomial (n,p) , where n=54, p=0.94

Here p=0.94 is the probability that a person will show up.

And 1-p = 1-0.94= 0.06 is the probability that a person will not show up

So, pmf of X is,

P(X=x)=54Cx × (0.94)x × (0.06)54-x  , x= 0,1 2,3,........,54.

P(50 or more people will show up)

= P(X=50)+P(X=51)+P(X=52)+P(X=53)+P(X=54)

=54C50 × (0.94)50 × (0.06)54-50 + 54C51 × (0.94)51× (0.06)54-51 + 54C52 × (0.94)52 × (0.06)54-52 + 54C53 × (0.94)53 × (0.06)54-53 + 54C54× (0.94)54 × (0.06)54-54

= 316251× (0.94)50 × (0.06)4  + 24804× (0.94)51× (0.06)3

+ 1431× (0.94)52 × (0.06)2 + 54× (0.94)53× (0.06) + (0.94)54

= 0. 7778