The probability is 0.03 that a passenger on United Airlines Flight 9841 is a Pla

ID: 3061303 • Letter: T

Question

The probability is 0.03 that a passenger on United Airlines Flight 9841 is a Platinum flyer (50,000 miles per year).

If 225 passengers take this flight, find the binomial and Poisson probability of no Platinum flyers. (Round your answers to 4 decimal places.)

If 225 passengers take this flight, find the binomial and Poisson probability of two Platinums flyer. (Round your answers to 4 decimal places.

If 225 passengers take this flight, find the binomial and Poisson probability of 3 Platinum flyers. (Round your answers to 4 decimal places.)

The probability is 0.03 that a passenger on United Airlines Flight 9841 is a Platinum flyer (50,000 miles per year).

The poisson distribuyion is related to binomial as h(poisson parameter)=n*p. The probability is respectively,

P(x)[Poisson]=h^x*e^(-h)/x! and Binomial P(x)=nCx*p^(x)*(1-p)^(n-x). Here h=225*.03=6.75.

a) P(x=0) for Poisson=e^(-6.75)=0.0011 and Binomial =(1-0.03)^225=.0010

b) P(x=2) for poisson=6.75^2*e^(-6.75)/2 =0.0266 and Binomial = 225*224/2*0.03^2*0.97^223=0.0254

c)P(x=3) for poisson=6.75^3*e^(-6.75)/6 =0.06 and Binomial = 225*224*223/6*0.03^3*0.97^222=0.0585

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