6) Adult's weight are normally distributed,mean is 155 lb, standard deviation is 31 lb. (a) If 5 adults are randomly selected, find the probability that their average weight is less than 170 lb. (b) If X¯¯¯¯X¯ (X-bar)represents the average weight for 10 adults, find the number k such that P(X-bar<0.995)=k. (c) You need to design an elevator, and it must safely carry 10 adult passengers. Find the maximum TOTAL allowable weight if we want a 0.995 probability that this maximum will not be exceeded when 10 adults are randomly selected.
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!
(6) Adult's weight are
(a) If 5 adults are randomly selected, find the
(b) If X¯¯¯¯X¯ (X-bar)represents the average weight for 10 adults, find the number k such that P(X-bar<0.995)=k.
(c) You need to design an elevator, and it must safely carry 10 adult passengers. Find the maximum TOTAL allowable weight if we want a 0.995 probability that this maximum will not be exceeded when 10 adults are randomly selected.
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