The central limit theorem
I was working this problem, and was curious how I add the "10% of the forms" portion to the problem.
Here is the problem:
Among all the income-tax forms filed in a certain year, the mean tax paid was $2000 and the standard deviation was $500. In addition, for 10% of the forms, the tax paid was greater than $3000. A random samlpe of 625 tax forms is drawn.
a. What is the probability that the average tax paid on the sample form is greater than $1980?
So I did P(X > 1980)
X = N(2000,400)
Z = (1980 - 2000)/sqrt(400) = -1
Z-table gives me a value of 0.1587 for -1. So 1 - 0.1587 = 0.8413 probability. But how do you factor in the 10% thing?
b. What is the probability that more than 60 of the sampled forms have a tax of greater than $3000?
Was not sure how to go about this one.
Any help is greatly appreciated, thanks!