Passengers died when a particular water taxi sank. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 196 lb and a standard deviation of 41lb. The water taxi that sank had a stated capacity of 25 passengers, and the boat was rated for a load limit of 3750lb. Complete parts (a) through (d) below a. the max mean weight is________________lb b. if the water is filled with 25 randomly selected men, what is the probability that thier mean weight exceeds the vlue from part (a)? c. after the water taxi sank, the weight assumptionswere revised so that the new capacity became 20 passengers. if the water taxi is filled wiwth 20 randomly seleed men, what is the probability tht their mean weight exceeds 187.5 lb, which is the max mean weight that does not cause the total load to exceed 3750ld. d. is the new caoacity of 20 passenger safe?
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!
Passengers died when a particular water taxi sank. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are
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