A department store has its own store credit card, where the monthly balance of customer's credit is found to be Normally distributed with a mean of $476 and a standard deviation of $150.Assume the conditions are satisfied. SHOW BRIEF WORKINGS TO SUPPORT YOUR ANSWERS.

a) What is the probability that one randomly chosen customer has less than $450 owing on their store credit card?[2 marks]

b) You are now told that a sample of size 36 is taken.What is the probability that this sample has an average less than $450 owing on their store credit card?[3 marks]