Can anyone please help me with this! I already answer these questions, but I jus
ID: 2923537 • Letter: C
Question
Can anyone please help me with this! I already answer these questions, but I just want to make sure if I did it right or not. Please show me the steps too. Thank you!
Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 9 passengers per minute.
a) Compute the probability of no arrivals in a one-minute period (to 6 decimals).
b) Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals).
c) Compute the probability of no arrivals in a 15-second period (to 4 decimals).
d) Compute the probability of at least one arrival in a 15-second period (to 4 decimals).
Explanation / Answer
POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.
x = is the number of independent trials
the mean arrival rate is 9 passengers per minute = mean =
= 9
I.
P( X = 0 ) = e ^-9 * 9^0 / 0! = 0.000123
II.
P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0) +
= e^-9 * 9 ^ 3 / 3! + e^-9 * 0 ^ 2 / 2! + e^-9 * ^ 1 / 1! + e^-9 * ^ 0 / 0!
= 0.0212
III.
Mean rate for 15 sec period = 9/4 = 2.25
P( X = 0 ) = e ^-2.25 * 2.25^0 / 0! = 0.1054
IV.
P( X < 1) = P(X=0)
= e^-2.25 * 1 ^ 0 / 0!
= 0.1054,
P( X > = 1 ) = 1 - P (X < 1) = 0.8946