SOLUTION: John parks cars at a hotel. On the average, 6.7 cars will arrive in an hour. Assume that a driver's decision on whether to let John park the car does not depend upon any other per

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Question 1075146: John parks cars at a hotel. On the average, 6.7 cars will arrive in an hour. Assume that a driver's
decision on whether to let John park the car does not depend upon any other person's decision.
Define the random variable x to be the number of cars arriving in any hour period.
a. What is the appropriate probability distribution for x? Explain how x satisfies the
properties of the distribution.
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Random, numbers proportional to time, discrete, could be theoretically infinite.
Poisson distribution with parameter 6.7
P(x)=exp^(-6.7)*6.7^x/x! for x between 0 and infinity.
P(5)=e^-6.7*6.7^5/5!=0.1385
no more than 5
do 0-4
for 0 it is 0.0012
for 1 it is 0.0082
for 2 it is 0.0276
for 3 it is 0.0617
for 4 it is 0.1034
The sum of the 6 values is 0.3406. ANSWER
This makes sense. The expected value is 6.7.