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Among all the income-tax forms filed in a certain year,

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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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:

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.

Step 2 of 2

Chapter 4.11, Problem 4E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Among all the income-tax forms filed in a certain year,

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