A large commercial website processes on average 2.56 credit card payments per minute. The number X of credit card payments processed in one?minute intervals can be modeled accurately with a Poisson distribution.
(a) Sketch the probability mass function of X for values of X between 0 and 10 (I suggest using technology to speed up the calculations; no need to show your work). Find the mean and variance of X.
(b)We plan on taking a random sample of 36 independently selected minutes. What is the probability that the total number of credit cards processed in this sample would be greater than 100?
(c) Explain what important theorem you relied on for this computation.