Golf balls must meet a certain standard of distance traveled in order to be used in a professional tournament. When the ball is hit by a mechanical device, under specific calibration, the ball may not travel farther than 291.2 yards in the air. From past data a certain manufacturer has determined that the distances traveled for the balls, it produces are normally distributed with a mean of 290 yards. What standard deviation, in yards, should the manufacturer require if they want 99% of balls they manufacture to meet the tournament standards?
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!
Golf balls must meet a certain standard of distance traveled in order to be used in a professional tournament. When the ball is hit by a mechanical device, under specific calibration, the ball may not travel farther than 291.2 yards in the air. From past data a certain manufacturer has determined that the distances traveled for the balls, it produces are
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