A half-century ago, the mean height of women in a particular country in their 20s was 63.8 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.51 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 28 of today's women in their 20s have mean heights of at least 65.08 inches?
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!
A half-century ago, the
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