Question

The number of people entering a security check-in lineup in a 15-minute interval at a medium sized airport can be modeled by the following probability model:

?(?=?)=?−16.6(16.6)??!?=0,1,2,⋯P(X=x)=e−16.6(16.6)xx!x=0,1,2,⋯

Part (a) What does 16.6 represent in the probability model? Select the most appropriate explanation below.

A. 16.6 represents how much skewed the distribution of values is.
B. 16.6 represents a weighted-average of the number of people who enter the a security check-in lineup every 15-minutes.
C. 16.6 is the rate at which people enter the security check-in lineup every 15 minutes.
D. 16.6 is the standard deviation of the distribution of people entering the security check-in lineup every 15-minutes.
E. 16.6 represents the average number of people who enter the a security check-in lineup every 15-minutes.


Part (b) Compute the probability that 16 people enter the security check-in lineup in a 15-minute interval. Use four decimals in your answer.

?(?=16)=

Part (c) Compute the probability that at least 4 people will enter the security check-in lineup in a 5-minute interval.

Part (d) In the past 15-minutes, you have been told that somewhere between 13 and 20 people, inclusive, have entered the security lineup. Compute the probability that this uncertain number is 17.

Answer 1

x	P(X=x)
13	0.072084
14	0.085471
15	0.094587
16	0.098134
17	0.095825
18	0.088372
19	0.077209
20	0.064084
Total	0.675767

check-in lineup every 15-minutes. E. 16.6 represents the average number of people who enter the a security check-in lineup every 15-minutes. Part (b) Compute the probability that 16 people enter the security check-in lineup in a 15-minute interval. Use four decimals in your answer. e-16616.616 P(X =16) = = 0.098134 16! used excel funcion poisson(16.16.6.0) Part (c) Compute the probability that at least 4 people will enter the security check-in lineup in a 5-minute interval. 16.6 2= *5 = 2.2 15 22-222.23 P(X<4) =1-2 = 0.180648 !! used excel funcion 1- poisson(3, 2.2.1) Part (d) In the past 15-minutes, you have been told that somewhere between 13 and 20 people, inclusive, have entered the security lineup. Compute the probability that this uncertain number is 17. 2-16.616.617 P(X =17|13 < X <20) = = 0.1418 Σ- 17! 20 -16616.6* x-13

A B 1 x 2 13 3 =A2+1 4 =A3+1 5 =A4+1 6 =A5+1 7 =A6+1 8 =A7+1 9 =A8+1 10 Total 11 12 Probabiiltiy 13 P(X=x) =POISSON(A2,16.6,0) =POISSON(A3,16.6,0) =POISSON(A4,16.6,0) =POISSON(A5,16.6,0) =POISSON(A6,16.6,0) =POISSON(A7,16.6,0) =POISSON(A8,16.6,0) =POISSON(A9,16.6,0) =SUM(B2:39) =B6/B10

check-in lineup every 15-minutes. E. 16.6 represents the average number of people who enter the a security check-in lineup every 15-minutes. Part (b) Compute the probability that 16 people enter the security check-in lineup in a 15-minute interval. Use four decimals in your answer. -16616.616 P(X =16) = = 0.098134 16! used excel funcion poisson(16.16.6.0) Part (c) Compute the probability that at least 4 people will enter the security check-in lineup in a 5-minute interval. 16.6 *5=5.53 15 35.53% P(X24)=1- P(X<4)=1- 0.801677 used excel funcion 1-poisson(3,5.53.1) 2= -5.53 - * 5:53 Part (d) In the past 15-minutes, you have been told that somewhere between 13 and 20 people, inclusive, have entered the security lineup. Compute the probability that this uncertain number is 17. e-16.616.617 P(X =1713 < X <20) = 17! -0.1418 e-16616.6* Σ x! = 20 2-13

A B 1 x 2 13 3 =A2+1 4 =A3+1 5 =A4+1 6 =A5+1 7 =A6+1 8 =A7+1 9 =A8+1 10 Total 11 12 Probabiiltiy 13 P(X=x) =POISSON(A2,16.6,0) =POISSON(A3,16.6,0) =POISSON(A4,16.6,0) =POISSON(A5,16.6,0) =POISSON(A6,16.6,0) =POISSON(A7,16.6,0) =POISSON(A8,16.6,0) =POISSON(A9,16.6,0) =SUM(B2:39) =B6/B10