Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal distribution with u = 28 pounds and o = 5.7 pounds. (a) Calculate the probability that a piece of luggage weighs less than 32.2 pounds. (Assume that the minimum weight for a piece of luggage is 0 pounds.) (b) Calculate the weight where the probability density function for the weight of passenger luggage is increasing most rapidly. Ib (c) Use the Empirical Rule to estimate the percentage of bags that weigh more than 16.6 pounds.
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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