Standard units tell you how many standard deviations above or below average a data value is standard units = (actual value – average)/SD actual value = average + (SD x standard units). Standard units are denoted by Z.

Chapter 8

Complement rule: P(A) = 1 – P(A doesn 't happen)

Multiplication rule:

P(A and B both happen) = P(A) x P(B given A happened)

Q. 5 random components removed one at a time from box containing 5 defective and twenty working. What is chance of selecting all defective:

A. 5/25x4/24x3/23x2/22x1/21. Selecting no defective 1 minus chance of selecting all defective or 20/25 x 19/24 x 18/23 x 17/22 x 16/21 = 2/7 or 29%

Q. Important data server breaks down 40% of the time, is operational the other 60%, and servers breakdown independently. How many independent servers should be running so that there is a 99% chance at least one is operational? (40%)^X = 1% (1% = chance none are operational)

A. .4^5 = .01024, so to get to .99 uptime, add another server.

Q. Consider two bonds with BB- ratings, chance of default 1.5%. What is the probability that both default within a year? A. .015 x .015 Q. What is the probability that neither defaults? A. .985 x .985 Q. What is the probability that exactly one defaults? A. P(exactly one) = 1 – P(neither) – P(both) = 1 - .015 x .015 - .985 x .985.

Independent: P(firm B defaults given A defaults) = P(firm B defaults) = .015

Dependant: P(firm A and B default) = P(firm A defaults) x P(firm B defaults given firm A defaults). = number greater than .015

Q. Janice has noticed that on her drive to work there are several things that can slow her down. First, she may hit a red light at a particular large intersection, which happens 30% of the time. If she hits the red light, 40% of the time she will have to stop for the commuter train. If she does not hit the red light, she only has to stop for the commuter train 20% of the time. we know P(red light)=.3, P(train| red light)=.4, P(train| no red