## Is it possible to estimate the uncertainty in these measurements?

1.  The Kilogram is now weighed five times on a different scale. The measurements are as follows, in units of micrograms above 1 kg: 25.6, 26.8, 26.2, 26.8, 25.4.

a.   Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not, explain why not.

b.   Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain why not.

2.   A new and unknown weight is weighed on the same scale that was used in Exercise 8, and the measurement is 127 μg above 1 kg. Using the information in Exercise 8, is it possible to come up with a more accurate measurement? If so, what is it? If not, explain why not.

3.  The article “Calibration of an FTIR Spectrometer” (P. Pankratz, Statistical Case Studies for Industrial and Process Improvement, SIAM-ASA, 1997: 19–38) describes the use of a spectrometer to make five measurements of the carbon content (in ppm) of a certain silicon wafer whose true carbon content was known to be 1.1447 ppm. The measurements were 1.0730, 1.0825, 1.0711, 1.0870, and 1.0979.

a.   Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not, explain why not.

b.   Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain why not.

### 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….