## Estimate the difference in the mean annual uplift between these two time periods, and find the uncertainty in the estimate.

1.  The length of a rod is to be measured by a process whose uncertainty is 3 mm. Several independent measurements will be taken, and the average of these measurements will be used to estimate the length of the rod. How many measurements must be made so that the uncertainty in the average will be 1 mm?

2.   The volume of a cone is given by V = πr 2h/3, where r is the radius of the base and h is the height. Assume the radius is 5 cm, measured with negligible uncertainty, and the height is h = 6.00 ± 0.02 cm. Estimate the volume of the cone, and find the uncertainty in the estimate.

3.   In the article “The World's Longest Continued Series of Sea Level Observations” (M. Ekman, Paleogeography, 1988:73–77), the mean annual level of land uplift in Stockholm, Sweden, was estimated to be 4.93 ± 0.23 mm for the years 1774–1884 and to be 3.92 ± 0.19 mm for the years 1885–1984. Estimate the difference in the mean annual uplift between these two time periods, and find the uncertainty in the estimate.

### 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….