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?
(a) Let 
be the amounts on the 625 bills.
Then 
is approximately normally distributed with mean 
.
The z-score of 500 is (500 ? 485)/10 = 1.50.
The area to the right of z= 1.50 is 1 ? 0.9332 = 0.0668.
.
(b) Let Y be the number of bills whose amount is greater than $1000.
Then Y?Bin(900, 0.15), so Y is approximately normal with mean 900(0.15) = 135 and standard deviation
To ?nd (Y>150), use the continuity correction and ?nd the z-score of 150.5.
The z-score of 150.5 is (150.5 ? 135)/10.712 = 1.45.
The area to the right of z=1.45 is 1 ? 0.9265 = 0.0735.
P(Y>150)=0.0735.
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