## Find the standard deviation of the thickness of an item.

1.  Two batteries, with voltages V1 and V2 , are connected in series. The total voltage V is given by V = V1 + V2 . Assume that V1 has mean 12 V and standard deviation 1 V, and that V2 has mean 6 V and standard deviation 0.5 V.

a.  Find μV . Assuming V1 and V2 to be independent,

b.  find σV .

2.   A laminated item is composed of five layers. The layers are a simple random sample from a population whose thickness has mean 1.2 mm and standard deviation 0.04 mm.

a.  Find the mean thickness of an item.

b.  Find the standard deviation of the thickness of an item.

3.  Two independent measurements are made of the lifetime of a charmed strange meson. Each measurement has a standard deviation of 7×10 −15 seconds. The lifetime of the meson is estimated by averaging the two measurements. What is the standard deviation of this 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….