×
×

# Among all the income-tax forms filed in a certain year, ISBN: 9780073401331 38

## Solution for problem 4E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Statistics for Engineers and Scientists | 4th Edition

4 5 1 321 Reviews
21
1
Problem 4E

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?

Step-by-Step Solution:

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.

Step 2 of 2

##### ISBN: 9780073401331

Unlock Textbook Solution