physical fitness association is including the mile run in its hight school fitness test. The time for this event is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. The fitness association wants to recognize students whose times are among the top (or fastest) 10% with certificates of recognition. What time would a student need to beat in order to earn a certificate of recognition from the fitness association? Round to one decimal place. A. 395.9 sec B. 377.8 sec C. 524.1 sec D. 542.2 s
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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