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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.11 - Problem 4e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.11 - Problem 4e

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# 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

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Problem 4E

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

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