Solution Found!
Among all the income-tax forms filed in a certain year,
Chapter 4, Problem 4E(choose chapter or 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 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?
Questions & Answers
QUESTION:
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:
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.