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 sample of 625 tax forms is drawn.

a. What is the probability that the average tax paid on the sample forms is greater than $1980?

b. What is the probability that more than 60 of the sampled forms have a tax of greater than $3000?

Answer:

Step 1 of 2:

(a)

In this question, we are asked to find the probability that the average tax paid on the sample forms is greater than .

The mean tax paid was and the standard deviation was .

In addition, for 10% of the forms, the tax paid was greater than

A random sample of 625 tax form is drawn.

Let denote the drawn tax forms.

We need to find

Now the sample size is , which is a large sample.

Hence can be approximately normal distributed.

CLT specifies that , variance and standard deviation

Hence our sample mean and standard deviation is,

= $20

Therefore the score of $1980 is

=

=

=

From the z table, the area to the left of is 0.1587.

The area to right of = -1 is 1 - 0.1587 = 0.8413.

Hence the probability that the average tax paid on the sample forms is greater than is 0.8413.