The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 68.5 with a standard deviation of 7.5. Assume that the distribution is approximately normal. a) Find the probability that an elite athlete has a maximum oxygen uptake of at least 90.3 ml/kg. b) Find the probability that an elite athlete has a maximum oxygen uptake of at most 59.5 ml/kg.
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!
The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 68.5 with a standard deviation of 7.5. Assume that the distribution is approximately normal. a) Find the
b) Find the probability that an elite athlete has a maximum oxygen uptake of at most 59.5 ml/kg.
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