State results to the accuracy level specified; if not specified, state to an accuracy based on the problem.

#### Problem (1)

Survey Crew A measured a distance multiple times: 118.54', 118.52', 118.48', 118.54', 118.53', 118.47'.

Determine

The most probable line length

Its standard deviation

The length's expected error

Compute all to 0.001'.

#### Problem (2)

Two crews measured different distances multiple times. There results, in feet, are shown in the table below:

 Crew A Crew B Num of meas 4 12 Average 87.96 108.53 Standard deviation ±0.030 ±0.035

Which Crew had better:

Precision?

Expected accuracy?

Explain why in both cases and support mathematically.

#### Problem (3)

The zenith angle to the top of a flag pole was measured with these results: 37°18'55", 37°19'04", 37°19'09", 37°18'53", 37°19'02"

Determine

The most probable zenith angle

Its standard deviation

The angle's expected error

Compute all to 0.1".

#### Problem (4)

The length and width of a building are measured in feet, summarized in the table below.

 Length Width 173.9 89.6 174.5 90.1 174.3 89.7

What are the building's area and expected area error in square yards?

#### Problem (5)

A lab technician was to determine the moisture content of a soil sample. She weighed the sample 4 times and obtained an average of 583.4 gr with a ±0.9 gr standard deviation. After the sample was dried for 24 hours at 400° F, she weighed it 6 times for an average of 552.9 gr and standard deviation of ±1.5 gr. What was the soil’s moisture content, and its expected error, in grams?

#### Problem (6)

If all angles are measured to the same level of accuracy and their total must be within 15 seconds of (n-2)x180°, how much error is allowed in each angle of a five-sided property?