Aa Aa E 2. The uniform distribution The Transportation Security Administration (

Question

Aa Aa E 2. The uniform distribution The Transportation Security Administration (TSA) collects data on wait time at each of its airport security checkpoints. For flights departing from Terminal 1 at John F. Kennedy International Airport (JFK) between 3:00 and 4:00 PM on Wednesday, the mean wait time is 10 minutes, and the maximum wait time is 12 minutes. [Source: Transportation Security Administration, summary statistics based on historical data collected between February 18, 2008, and March 17, 2008.] Assume that x, the wait time at the Terminal 1 checkpoint at JFK for flights departing between 3:00 and 4:00 PM on Wednesday, is uniformly distributed between 8 and 12 minutes. Use the Distributions tool to help you answer the questions that follow. Uniform 30 Minimum 8.0 24 18 Maximum 12.0 12 06 00 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 The height of the graph of the probability density function f(x) varies with x as follows (round to four decimal places):

Explanation / Answer

1.) Height of the graph of the probability density function: x<8= 0 (because the probability ofx<8=0); 8<x<12=0.25 ( because probability that 8<x<12 is 1 and divided by 4 units(12-8) equally as it is a uniform distribution; x>12=  0 (because the probability of x>12=0)

2.)P(X>11)= the probability that I will miss the flight which is equal to 0.25

3.) Mean time=1/2(8+12)=10

Standard Deviation=1/12(12-8)^2=16/12=4/3=1.33

4.) P(X>11 given X>9)=P(X>11&9)/P(X>9)=P(X>11)/P(X>9)=0.25/.75=0.3333

5.) Interquarile range is the difference between the third and the first quartile=11-9=2

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