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During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7...

During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7 customers every 5 minutes. assume a poisson distribution to find the probability that:

A) exactly 12 customers arrive in a given 10 minute interval (perform this calculation using an appropriate formula, showing the setup.)

b) between 5 and 10 customers (inclusive) arrive in a given 5 minute interval (show how you can answer this from the table)

c) after a customer arrives, find the probability that at least one customer arrives in the next 2 minutes.

d) if the random variable x is a poisson r.v. counting the number of customers in a 5 minute interval, then find the value of E(x^2). use the short cut formula for variance

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