A woman parks her car and puts in enough money to cover her for one hour....
A woman parks her car and puts in enough money to cover her for one hour. She is waiting on line at the DMV and there are 14 people ahead of her on the line. We assume that the time that each customer spends with the DMV agent is independent of the time spent by any other customer and is normally distributed with mean 4 minutes and a standard deviation of 1.5 minutes. If it takes her 2 minutes to walk to the DMV and 2 minutes to return to her car, what is the probability that she will get back to her car before her meter expires?
Homework Answers
we need
Xi = time spent
Y = X1 + X2+ ..X15 < 60 - 2-2
Xi = N(4 ,1.5^2)
X1 + ..X15 = N(4 *15 , 15 * 1.5^2)
= N(60 , 33.75 )
P(Y < 56)
= P(Z <( 56 - 60)/sqrt(33.75))
= P(Z < -0.68853 )
= 0.2456
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1
2
3
4
5
0.1
0.0111
0.15
0.0264
0.0008
0.2
0.05
0.002
0.25
0.0833
0.0039
0.3
0.1285
0.0069
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0.1884
0.011
0.4
0.2666
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0.45
0.3681
0.0239
0.0019
0.5
0.5
0.0333
0.003
0.55
0.6722
0.0449
0.0043
0.6
0.9
0.0593
0.0061
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Table: Average Number of Customer in Waiting
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Poisson Arrivals, Exponential Service Times
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