## 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?

### 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….