A sign is posted in an elevator stating that the maximum number of people allowed is 25, and that the maximum weight capacity is 4000lbs. Suppose the distribution of the variable Weight (among the population using the elevator) is normal with mean 150lbs and standard deviation 30lbs. What is the probability that a randomly selected group of 25 people will exceed the maximum weight capacity? What should the maximum number of people allowed be if the probability of the maximum weight capacity being exceeded is to be at most .00001?
SD : sd / sqrt(n) = 30/5 = 6
mU : 150
avg (x) : 4000 / 25 = 160
p(x > 4000) = 1 - phi[(160 - 1/2 - 150) / 6]
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