Shen, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fall down a sandstone cliff beside a main highway. As part of an accident simulator, Shen models the boulders' weights using a normal distribution with a mean of 565 kg and a standard deviation of 150 kg. Use this table or the ALEKS calculator to find the percentage of boulders that weigh between 733 kg and 859 kg according to the model. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example 98.23%).
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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