Question
In: Statistics and Probability
the number of cars arriving at a bank car service between 3:00 pm and 6:00 pm...
the
number of cars arriving at a bank car service between 3:00 pm and
6:00 pm on Friday, according to a Poisson process at the rate of
0.3 cars per minute. Calculate the probability that at least 4 cars
arrive at the bank between 4:00 pm and 4:10 pm
Solutions
Expert Solution
Answer:-
Given that:-
The number of cars arriving at a bank car service between 3:00 pm
and 6:00 pm on Friday, according to a Poisson process at the rate
of 0.3 cars per minute. Calculate the probability that at least 4
cars arrive at the bank between 4:00 pm and 4:10 pm
The number of cars arriving at a bank car service between 3:00 pm and 6:00 pm on Friday, according to a Poisson process at the rate of 0.3 cars per minute.
X: Random variable denoting that the number of cars arriving per
minute .i.e.
Now we want to calculate the probability that fewer than 4 cars arrive at the bank between 4:00pm and 4:10 0.m i.e time interval is 10 minute . Now if X random variable denoting by,
X: Random variable denoting that the number of cars arriving between 4:00 p.m and 4:10 p.m i.e in 10 minute
i.e 
So PMF of X is given by,
where ,
Now our required probability is given by,
The probability that at least 4 cars arrive at the bank between 4:00 pm and 4:10 pm is 0.6472
orchestra answered 2 years agoRelated Solutions
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Missing
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A random sample of 100 customers was chosen in a market between 3:00 and 4:00 PM...
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2.0-2.9
3.0-3.9
4.0-5.9
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8
22
Missing
Missing
Missing
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Missing
Missing
0.84
0.98
1.00
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Historically, the number of cars arriving per hour at Lundberg’s Car Wash is observed to be...
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4
10
5
30
6
50
7
65
8
45
Total:
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