An elevator has a placard stating that the maximum capacity is 1640 lb-10 passengers. So, 10 adult male passengers can have a mean weight of up to 1640/ 10 = 164 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 164 lb. (Assume that weights of males are normally distributed with a mean of 173 lb and a standard deviation of 34 lb.) Does this elevator appear to be safe? The probability the elevator is overloaded is. (Round to four decimal places as needed.)
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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