2. Using the unitorm distribution Aa checkpoints. For flights departing from Ter

Question

2. Using the unitorm distribution Aa checkpoints. For flights departing from Terminal 9 at John F. Kennedy International Nrport (3FK) between 3:00 and 4:00 PM on Wednesday, the mean wait tme is 10 minutes, and the maximum wait time is 18 minutes fSource Transportation Security Administration, summary statistics based on historical data collected between lanuary s, 2008, and February 5, 2008.1 Assume that X, the wait time at the Terminal 9 checkpoint at JFK for fights departing between 3:00 and 4:00 Pt Wednesday, is uniformily distributed between 2 and 18 minutes Use the Distributions tool to help you answer the questions that follow -10 Minimum K 125 e o o The height ot the graph of the probabitity density function fo) varies with X as follows (round to four decimat places) Height of the Graph of the Probability Density Function x x> 18 You are thying out of Terminat 9 at JFK on a wednesday aftemoon between 3:00 and 4:00 PM. You get stuck in a traffic jam on thie way to the alrport, and if it takes you longer than 12 minutes to clear securty, you miss your fight. T your night is You have arrived at the airport and have been waiting 8 minutes at the security checkpoint. Recat tnat if you spend mare than 12 minutes clearing security, you will niss your right. Now what is the probabitlty that you's miss your right? 0 0.3333 O 0.8333 11/7/201

Explanation / Answer

2.

UNIFORM DISTRIBUTION
PDF of uniform distribution f(x) = 1 / ( b - a ) for a < x < b
b = maximum Value
a = minimum Value
f(x) = 1/(b-a) = 1 / (18-10) = 1 / 8 = 0.125
I.
mean = a + b / 2
=(10+18)/2
=14
II.
standard deviation = sqrt ( ( b - a ) ^ 2 / 12 )
=sqrt(18-10)^2 / 12
=2.3094
a.
P(X < 2) = (2-10) * f(x)
= -8*0.125
= -1
b.
To find P(a < X < b) =( b - a ) * f(x)
P(2 < X < 18) = (18-2) * f(x)
= 16*0.125
= 2
c.
P(X > 18) = (18-18) * f(x)
= 0*0.125
= 0
d.
stuck at traffic jam on the way to airport.you will miss the flight,it takes more than 12 min clear the security.then
probability will miss flight
P(X > 12) = (18-12) * f(x)
= 6*0.125
= 0.75
e.
you have arrived the airport but 8 min wait at security check for recall spend it takes more than 12 min then you will miss the flight
probabilty that you will miss the flight
P(X > 12) = (18-12) * f(x)
= 6*0.125
= 0.75

=0.8

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