1. In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective,….

## Estimate v, and find the uncertainty in the estimate.

1. The resistance R (in ohms) of a cylindrical conductor is given by R = kl/d 2 , where l is the length, d is the diameter, and k is a constant of proportionality. Assume that l = 14.0 ± 0.1 cm and d = 4.4 ± 0.1 cm.

a. Estimate R, and find the uncertainty in the estimate.

b. Your answer will be in terms of the proportionality constant k.

c. Which would provide the greater reduction in the uncertainty in R: reducing the uncertainty in l to 0.05 cm or reducing the uncertainty in d to 0.05 cm?

2. Refer to Exercise 16. In an experiment to determine the value of k, the temperature T at time t = 10 min is measured to be T = 54.1 ± 0.2°F. Assume that T0 = 70.1 ± 0.2°F and Ta = 35.7 ± 0.1°F. Estimate k, and find the uncertainty in the estimate.

3. The vertical displacement v of a cracked slurry infiltrated fiber concrete member at maximum shear stress is given by v = a + bw, where w is the crack width, and a and b are estimated from data to be a = 2.5 ± 0.1 mm and b = 0.05 ± 0.01. Assume that w = 1.2 ± 0.1 mm.

a. Estimate v, and find the uncertainty in the estimate.

b. Of the uncertainties in w, a, and b, only one has a non-negligible effect on the uncertainty in v. Which one is it?