uppose an elevator has a maximum capacity of 16 passengers with a total weight of 2500lbs. Assume that weights of women are normally distributed with a mean of 168.4 lbs and a standard deviation of 29lbs A. Find the probability that 1 randomly selected woman has a weight greater than 156.25lbs b. Find the probability that the sample of 16 women have a mean weight greater than 156.25lbs (which puts the total weight at 2500lb, exceeding the maximum capacity)
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!
Suppose an elevator has a maximum capacity of 16 passengers with a total weight of 2500lbs. Assume that weights of women are
A. Find the
b. Find the probability that the sample of 16 women have a mean weight greater than 156.25lbs (which puts the total weight at 2500lb, exceeding the maximum capacity)
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