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5/31/2011
FINAL EXAMINATION  STAT 427
1. [25 points]
During slack periods, trucks arrive independently at a weighing station at an
average rate of 10 per hour. Suppose that with probability 0.95 an arriving truck will have
no overweight violations.
a)
[5 points]
What is the distribution of total time between any four consecutive trucks
entering the inspection station?
b)
[8 points]
Find the probability that two or more trucks enter the station during a
randomly selected 15minute period and none of these have overweight violations.
c)
[4 points]
Less than one vehicle entering the station in any 15minute period leads to
the early closure of the station at the end of the period. The station is monitored during
40 independent 15minute periods over various days. Let Y denote the number of times
that the station is closed for the day among these 40 trials. What is the distribution of
Y?
d)
[8 points]
The slack duration of 10 hours in a day is divided into 40 consecutive non
overlapping 15minute periods. Less than one vehicle entering the station in a period
leads to the early closure of the station for the day. If the station doesn’t close early, it
closes for the day automatically at the end of the 10 hour period. For
1,2,
,40
i
,
th
1,
if the station is closed in the i period,
0,
otherwise.
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 Spring '09
 Statistics, Probability, Probability theory, probability density function, Corr

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