During the 2011–12 NBA season, LeBron James had anaverage of 30.3 points per game. The mean and standarddeviation for the league were 7.65 points per game and6.64 points per game, respectively. That same season theWNBA was led by two players; both Diana Taurasi andAngel McCoughtry averaged 21.6 points per game. Themean and standard deviation for the entire WNBA thatyear were 8.13 points per game and 4.77 points per game,respectively. Which is the more remarkable performancecompared to the rest of their league? A) LeBron James had the more remarkable performancebecause he scored more points than the womenplayers did.B) LeBron James had the more remarkable performancebecause the means show that it’s harder to scorepoints in the NBA.C) Diana Taurasi and Angel McCoughtry had the more remarkable performances because the standard devia-tions show that there’s less variability in scoring in the WNBA.D) LeBron James had the more remarkable performancebecause his average was more standard deviationsabove the mean than the women’s average.E) You cannot compare these performances because thetwo leagues are so different.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
During the 2011–12 NBA season, LeBron James had an
average of 30.3 points per game. The
deviation for the league were 7.65 points per game and
6.64 points per game, respectively. That same season the
WNBA was led by two players; both Diana Taurasi and
Angel McCoughtry averaged 21.6 points per game. The
mean and standard deviation for the entire WNBA that
year were 8.13 points per game and 4.77 points per game,
respectively. Which is the more remarkable performance
compared to the rest of their league?
because he scored more points than the women
players did.
B) LeBron James had the more remarkable performance
because the means show that it’s harder to score
points in the NBA.
C) Diana Taurasi and Angel McCoughtry had the more
tions show that there’s less variability in scoring in
D) LeBron James had the more remarkable performance
because his average was more standard deviations
above the mean than the women’s average.
E) You cannot compare these performances because the
two leagues are so different.
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