## Estimate f, and find the uncertainty in the estimate.

1.  The lens equation says that if an object is placed at a distance p from a lens, and an image is formed at a distance q from the lens, then the focal length f satisfies the equation 1/f = 1/p + 1/q. Assume that p = 2.3 ± 0.2 cm and q = 3.1 ± 0.2 cm.

a.  Estimate f, and find the uncertainty in the estimate.

b.  Which would provide a greater reduction in the uncertainty in f: reducing the uncertainty in p to 0.1 cm or reducing the uncertainty in q to 0.1 cm?

2.    The pressure P, temperature T, and volume V of one mole of an ideal gas are related by the equation PV = 8.31 T, when P is measured in kilopascals, T is measured in kelvins, and V is measured in liters.

a.   Assume that P = 242.52 ± 0.03 kPa and V = 10.103 ± 0.002 L. Estimate T, and find the uncertainty in the estimate.

b.  Assume that P = 242.52 ± 0.03 kPa and T = 290.11 ± 0.02 K. Estimate V, and find the uncertainty in the estimate.

c.    Assume that V = 10.103 ± 0.002 L and T = 290.11 ± 0.02 K. Estimate P, 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….