1.    Refer to Exercise 5. Assume that the relative uncertainty in P1 is 5% and the relative uncertainty in P2 is 2%. Find the relative uncertainty in P3.

2.    Refer to Exercise 14. Assume that the relative uncertainty in l is 3% and that the relative uncertainty in d is 2%. Find the relative uncertainty in R.

3.   An item is to be constructed by laying three components in a row. The length of each component will be measured.

a.  If the uncertainty in measuring the length of each component is 1.2 mm, what is the uncertainty in the combined length of the three components?

b.  If it is desired to estimate the length of the item with an uncertainty of 0.5 mm, what must be the uncertainty in the measurement of each individual component? Assume the uncertainties in the three measurements are the same.

4.    For some genetic mutations, it is thought that the frequency of the mutant gene in men increases linearly with age. If m1 is the frequency at age t1 , and m2 is the frequency at age t2 , then the yearly rate of increase is estimated by r = (m2 − m1 )/(t2 − t1 ). In a polymerase chain reaction assay, the frequency in 20-year-old men was estimated to be 17.7 ± 1.7 per µg DNA, and the frequency in 40-year-old men was estimated to be 35.9 ± 5.8 per µg DNA. Assume that age is measured with negligible uncertainty.

a.  Estimate the yearly rate of increase, and find the uncertainty in the estimate.

b.   Find the relative uncertainty in the estimated rate of increase.