The probability is 006 that a passenger on United Airlines f

The probability is 0.06 that a passenger on United Airlines flight 9841 is a Platinum flyer (50,000 miles per year)

a.) If 110 passengers take this flight, find the binomial and Poisson probability of no platinum flyers

b.) If 110 passengers take this flight, find the binomial and Poisson probability of 2 platinum flyer

c.) Is the Poisson approximation justified?

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where     
k = number of successes in trials        
n = is the number of independent trials        
p = probability of success on each trial

a)
P( X = 0 ) = ( 110 0 ) * ( 0.06^0) * ( 1 - 0.06 )^110
= 0.0011

b)
P( X = 2 ) = ( 110 2 ) * ( 0.06^2) * ( 1 - 0.06 )^108
= 0.027

c)
NO