Assume that the total number of claims an insurance company receives each day follows a poisson distribution with parameter 1000. for each claim received, there is a probability of 0.2 that the company will not make a payment. (hint: given the number of claims for a day, the number of payments follows a binomial distribution.)

(a) what is the expected number of payments each day for this company?

(b) find the standard deviation for the number of payments each day for this company.