a) A Bank receives an average of 20 customers per hour. It is assumed that the number of customers received to follow a Poisson distribution.

i) Calculate the probability of receiving at least 7 customers in 15 minutes?

ii) What is the probability that less than 8 customers are received in 30 minutes?

Question 2 ([3 + 2] + [2 + 3] = 10 marks) a) A Bank receives an average of 20 customer per hour. It is assumed that the number of customers received follow a Poisson distribution. i) Calculate the probability of receiving at least 7 customers in 15 minutes? Let x = the number of customers received follow a Poisson distribution Mean = P (m: >=7) = (max >= ii) What is the probability that less than 8 customers are received in 30 minutes? P (W8) b) The proportion of female customers in a branch of Westpac is 40%. Determine: 1) What is the probability that a randomly selected sample of 200 customers in the same branch, less than 60 of them are female