A distance is measured through mountainous terrain and found to be 5182.40 ft. If on the average a plumb bob is used every 50 ft with a probable error of '0.02 ft, what is the probable total error in the whole distance?

Answer: probable error in the measurement is 2.073 ft.

So, real measurement is (5182.40 ± 2.073) ft

Step-by-step explanation:

Errors are additive. Therefore, if each 50 ft measured has a probable error of 0.02 ft,

The probable error in measuring 5182.4 ft has to be the amount of (50 ft in 5182.40 ft) * 0.02.

That is, probable error in measuring 5182.40 ft = (5182.40/50) * 0.02 = 2.07296 ft = 2.073 ft.

QED!