In Major League Baseball, the average fastball pitch is 90 miles per hour, μ = 90, with a standard deviation of 3 miles per hour, σ = 3. Solve these problems by using the Area Under the Curve Table and a handheld calculator. Then answer these questions using the Excel file,
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!
In Major League Baseball, the average fastball pitch is 90 miles per hour, μ = 90, with a standard deviation of 3 miles per hour, σ = 3. Solve these problems by using the Area Under the Curve Table and a handheld calculator. Then answer these questions using the Excel file,
- A)A pitcher’s fastball is 96 miles per hour. Is he among the fastest 1 percent of pitchers?
- B)A pitcher’s fastball is 95 miles per hour. Is he among the fastest 5 percent of pitchers?
- C)A pitcher’s fastball is 85 miles per hour. Is he among the slowest 2.5 percent of pitchers?
- D)A pitcher’s fastball is 80 miles per hour. Is he among the slowest 1 percent of pitchers?
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