Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 258 feet and a standard deviation of 58 feet. We randomly sample 49 fly balls. Find the 80th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)|
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!
Let be the average distance of fly ball hit to the outfield.
The 80th percentile of the distribution of the average of 49 fly balls is,
The probability 0.80 would be converted to z score can be obtained using the excel formula “=NORM.S.INV(0.80)”. The z score value is 0.8416.
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