Among all monthly bills from a certain credit card company, the mean amount billed was \(\$ 485\) and the standard deviation was \(\$ 300\). In addition, for \(15 \%\) of the bills, the amount billed was greater than \(\$ 1000\). A sample of 900 bills is drawn.

a. What is the probability that the average amount billed on the sample bills is greater than \(\$ 500\) ?

b. What is the probability that more than 150 of the sampled bills are for amounts greater than \(\$ 1000\) ?