# Homework 2 ### Due

: Thursday Sept 12 beginning of class

Note: To work this assignment out, students are expected to study the textbook sections specified below and the corresponding class notes (PowerPoint slides).

### Random Errors in Engineering Measurements

Read sections 1-15 through 1-18 and sections A.1 to A.7 in Appendix A in the textbook and work the following problems:

1. (10 points) The area of a parking lot is calculated to be 5,474 ft

2

with an estimated standard deviation of 2 ft

2

. What is the Maximum Anticipated Error? There is a 90% chance that the error range will be what?

2. (10 points) Examine Figure A.3 page 700 for the 95% error. What area is under the “minus tail”?

What area is above the “plus tail”?

3. (10 points) An engineer uses a standard technique for measuring the thickness of a clay landfill liner that has a typical standard deviation of 0.7 inches. The project specifications require the liner thickness to be 36 inches or more, at least 95 percent of the time. This means that the “minus tail” of the normal distribution curve of these measurements must have an area of 5 percent. What average thickness must the engineer build to meet these specifications?

4. (10 points) If the accidental error is estimated to be

0.006 ft for each of 24 separate distance measurements, what is the standard error of the sum of these measurements?

5. (10 points) For a 9-sided closed landscaped area, the sum of the interior angles should be exactly

1260

. It is specified for a survey of this area that if these angles are measured in the field, their sum should not deviate from 1260

by more than

1.0 minute. What error would you allow in the measurement of each individual angle?

6. (10 points) A rectangular field has an average length of 800 ft (with a standard error of 0.05 ft) and an average width of 300 ft (with a standard error of 0.03 ft). What is the area of the field? What is the standard error of the area?

### Error in EDMs

Read sections 3-21 through 3-24 in the textbook and work:

7. (15 points) If the manufacturer of a particular EDM states that the purported accuracy of the instrument is

(2 mm + 2 ppm), what error can be expected if the distance measured is 10 meters? 100 meters? 1,000 meters?

8. (15 points) In Problem # 7, what is the accuracy ratio for the 10 meter measurement? The 100 meter measurement? And the 1000 meter measurement?

9. (10 points) Work Problem 3.27 in the textbook.

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