A physical fitness test was given to a large number of college freshmen in part of the test each student was asked to run as far as he or she could in 10 minutes. The distance each student can ran in miles was recorded and can be considered as a random variable, say X. The data showed that the random variable X followed the log-normal distribution with ty = 0.35 and oy = 0.5, where Y = In X. A student is considered to be physically fit if he or she is able to run 1.5 miles in the allowed time. What is the percentage of the college starters would be considered physically fit if we consider only this part of the test?
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!
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