What a dense book! I enjoyed it and dreaded it. It has interesting details, yet is quite heavy in statistics. I encourage anyone who wants to see how stats can be used in life to read this book: Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football by Wayne L. Winston.
z score = (data point - mean)/(standard deviation)
For example, what is more unusual: the stock market dropping 22% on October 19, 1987 or seeing a person shorter than 30in tall walk down the street?
z score for Stock Market = (-22 - 0)/1.5 = -14.67
z score for short male = (30 - 69)/4 = -9.75
So the stock market change is much more unusual!
Independent events means knowing one result gives no insight into the other.
To calculate, you multiple the probability of each.
For example, what is the probability a pitcher with OBP of 0.34 pitches a perfect game. They need to strike out 27 batters. Each batter is independent and has a probability of 0.34.
Probability is = (1 - 0.34)\^27 = 0.0000134 or 1 in 74,500!
Use regressions to try to predict a dependent variable from a group's data.