SOLUTION: Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. a. Determine the expected number of customer arrivals for a five-minute perio

Question 1175125: Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.
a. Determine the expected number of customer arrivals for a five-minute period. (hint: this is the u)
b. If X = the number of arrivals per minute:
Find the probability of 10 customers or less arriving within a minute.
c. Find the probability of more than 7 customers arriving within a minute.
d. Find the probability of 3 customers arriving within a minute.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It is proportional to time, so lambda, the mean, is 15 for 5 minutes
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This is easier to look at the probability more than 10 will arrive within a minute, because it is expected to be small.
for 11 *e^(-3)^3^11/11!=0.0002
for 12 probability is 0.000055
the sum rounded is 0.0003
answer is 1- that or 0.9997
can check using poissoncdf(3,10)
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fewer than 8 per minute is the complement of c
that is 0.9880 probability
more than 7 customers a minute is 0.0120 probability
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this is e^(-3)*3^3/3!=0.2240 probability

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