Basis for the Range Rule of Thumb and the Empirical Rule. In Exercise, find the indicated area under the curve of the standard normal distribution, then convert it to a percentage andfill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-3. About_____% of the area is between 3 and z = −3 3 and z=3 and 3 (or within 3 standard deviation of the mean).
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!
Basis for the
About_____% of the area is between 3 and z = −3 3 and z=3 and 3 (or within 3 standard deviation of the mean).
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