Suppose that the amount of time it takes the IRS to refund to taxpayers is normally distributed with a mean of 12 weeks and a variance of 9.
a. What percent of taxpayers should get a refund within 5 weeks?
b. What percent of taxpayers will get their refund within 10-15 weeks?
c. How long will it be before 90% of the taxpayers get their refund?
d. If 10 independent taxpayers filed their refunds on the same day, what is the probability that at least 7 will get their refunds within 5 weeks?
e. What is the probability that the average time to get the refund for these 10 taxpayers (in c) is more than 13 weeks? (Not required. Bonus points if solved correctly.)
a,b. Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability for the Z score. Multiply by 100.
c. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.90) and its Z score insert into equation above.