In June 2009, the average Australian credit card account balance was $3,127, according to data extracted Assuming that these balances are approximately Normally distributed with a mean of $3,127 and a standard deviation of $1,500:
(a) Find the probability that an account balance is less than $2,000. Use a diagram!
Clearly indicate any properties of the Normal distribution that you are using to facilitate your calculation.
(b) One quarter of credit card accounts carry at least what balance? Use a diagram!
(c) Suppose that 100 credit card account balances are randomly selected. What is the probability that the average account balance in this sample is greater than $3,200? Use a diagram! What quantity must be approximately Normal for this calculation?