Prob Stat measure uncertainty If we measure the length of a

Prob Stat: measure uncertainty

If we measure the length of a pole, L, to be 25 cm ± 2 cm, and we use this measurement to calculate W = 3L + 5 = 80, the uncertainty is approximately:

The answer is 6cm but I do not understand how to get to this point. Help!

Solution

Note that as

E(L) = uncertainty of L = 2 cm

and

W = 3L + 5

Then

E(W) = 3*E(L)

(As you can see, the 5 does not matter, because 5 has 0 uncertainty.) Thus,

E(W) = 3*2 cm = 6 cm [ANSWER]