The heights of two year old females is approximately normally distributed with a mean of 33.7 inches and a standard deviation of 4.2 inches. If 750 females that are two years of age are randomly chosen then how many would we expect to be shorter than 24.5 inches or taller than 46.1 inches. Give your answer to two decimal places and do not give units.
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 heights of two year old females is approximately
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