The number of customers who arrive at a bank every 5 minutes has a Poisson distribution with a mean of 3.2. It is known that on a given day 720 clients arrive at the bank, a random sample of 40 of them is selected, then:

Write your answer rounding to three decimal places:

a) The standard error of the sample average of clients is: ____

b) The probability that the average number of sample customers who arrive at the bank branch every 5 minutes exceeds 3.7 is: ____

I can only use these topics: Exponential Distribution, Normal Distribution, Reproductive Property of the Normal Distribution, Sample Mean Distribution, and Central Limit Theorem