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?

 

find the cost of your paper

What is the probability that the parcel was shipped express and arrived the next day?

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,….

Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a.  Assume that….

If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26. a.  If a man tests negative, what is the probability that he actually has the disease? b.  For many medical tests, it is standard procedure….