The Transportation Security Administration (TSA) collects dataon wait time at each of its airport security checkpoints. Forflights departing from Terminal 3 at John F. Kennedy InternationalAirport (JFK) between 3:00 and 4:00 PM on Wednesday, the mean waittime is 12 minutes, and the maximum wait time is 16 minutes.[Source: Transportation Security Administration, summary statisticsbased on historical data collected between February 18, 2008, andMarch 17, 2008.]
Assume that x, the wait time at the Terminal 3 checkpoint at JFKfor flights departing between 3:00 and 4:00 PM on Wednesday, isuniformly distributed between 8 and 16 minutes.
Use the Distributions tool to help you answer the questions thatfollow.
0123NormalStandard NormalUniform
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The height of the graph of the probability density function f(x)varies with X as follows (round to four decimal places):
X | Height of the Graph of the Probability Density Function |
|---|
| X < 8 | |
| 8 ≤ X ≤ 16 | |
| X > 16 | |
You are flying out of Terminal 3 at JFK on a Wednesday afternoonbetween 3:00 and 4:00 PM. You get stuck in a traffic jam on the wayto the airport, and if it takes you longer than 12 minutes to clearsecurity, you’ll miss your flight. The probability that you'll missyour flight is-------------------- .
You have arrived at the airport and have been waiting 10 minutesat the security checkpoint. Recall that if you spend more than 12minutes clearing security, you will miss your flight. Now what isthe probability that you'll miss your flight?
a. 0.25
b. 0.6667
c. 0.5
d. 0.8333
An automobile battery manufacturer offers a 39/50 warranty onits batteries. The first number in the warranty code is thefree-replacement period; the second number is the prorated-creditperiod. Under this warranty, if a battery fails within 39 months ofpurchase, the manufacturer replaces the battery at no charge to theconsumer. If the battery fails after 39 months but within 50months, the manufacturer provides a prorated credit toward thepurchase of a new battery.
The manufacturer assumes that X, the lifetime of its autobatteries, is normally distributed with a mean of 44 months and astandard deviation of 3.6 months.
Use the following Distributions tool to help you answer thequestions that follow. (Hint: When you adjust the parameters of adistribution, you must reposition the vertical line (or lines) forthe correct areas to be displayed.)
0123BinomialChi-SquareExponentialFDistributionHypergeometricNormalUniform
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If the manufacturer’s assumptions are correct, it would need toreplace------------------------of its batteries free of charge.
The company finds that it is replacing 9.34% of its batteriesfree of charge. It suspects that its assumption about the standarddeviation of the life of its batteries is incorrect. A standarddeviation of---------------results in a 9.34% replacement rate.
Using the revised standard deviation for battery life, whatpercentage of the manufacturer’s batteries don’t qualify for freereplacement but do qualify for the prorated credit?
a. 84.95%
b.44.29%
c. 40.66%
d. 5.71%
