## Find the uncertainties in the following quantities

1.  The length of a rod was measured eight times. The measurements in centimeters, in the order they were taken, were 21.20, 21.22, 21.25, 21.26, 21.28, 21.30, 21.32, 21.35.

a.  Do these measurements appear to be a random sample from a population of possible measurements? Why or why not?

b.  Is it possible to estimate the uncertainty in these measurements? Explain.

2.   Assume that X and Y are independent measurements with uncertainties σX = 0.3 and σY = 0.2. Find the uncertainties in the following quantities:

a.   4X X + 2Y

b.   2X − 3Y

3.   A measurement of the diameter of a disk has an uncertainty of 1.5 mm. How many measurements must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm?

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