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 y, and find the uncertainty in the estimate.
1. Refer to Exercise 12 in Section 3.2. Assume that τ0 = 50 ± 1 MPa, w = 1.2 ± 0.1 mm, and k = 0.29 ± 0.05 mm−1 .
a. Estimate τ, and find the uncertainty in the estimate.
b. Which would provide the greatest reduction in the uncertainty in τ: reducing the uncertainty in τ0 to 0.1 MPa, reducing the uncertainty in w to 0.01 mm, or reducing the uncertainty in k to 0.025 mm−1?
c. A new, somewhat more expensive process would allow both τ0 and w to be measured with negligible uncertainty. Is it worthwhile to implement the process? Explain.
2. According to Snell's law, the angle of refraction θ2 of a light ray traveling in a medium of index of refraction n is related to the angle of incidence θ1 of a ray traveling in a vacuum through the equation sin θ1 = n sin θ2 . Assume that θ1 = 0.3672 ± 0.005 radians and θ2 = 0.2943 ± 0.004 radians. Estimate n, and find the uncertainty in the estimate.
3. Archaeologists studying meat storage methods employed by the Nunamiut in northern Alaska have developed a Meat Drying Index. Following is a slightly simplified version of the index given in the article “A Zooarchaeological Signature for Meat Storage: Rethinking the Drying Utility Index” (T. Friesen, American Antiquity, 2001:315–331). Let m represent the weight of meat, b the weight of bone, and g the gross weight of some part of a caribou. The Meat Drying Index y is given by y = mb/g. Assume that for a particular caribou rib, the following measurements are made (in grams): g = 3867.4 ± 0.3, b = 1037.0 ± 0.2, m = 2650.4 ± 0.1.
a. Estimate y, and find the uncertainty in the estimate.
b. Which would provide the greatest reduction in the uncertainty in y: reducing the uncertainty in g to 0.1 g, reducing the uncertainty in b to 0.1 g, or reducing the uncertainty in m to 0?