The Newport Varsity Club has 210 members. The weights of membershave a distribut

Question

The Newport Varsity Club has 210 members. The weights of membershave a distribution that is approximately normal with a mean of 163lb and a standard deviation of 32 lb. The design for a new clubbuilding includes an elevator with a capacity limited to 12passengers.
c. If the elevator is filled with 12 randomly selected clubmembers, what is the probability that the total load exceeds thesafe limit of 2100 lb? It his probability low enough?
d. What is the maximum number of passengers that should beallowed if we want a 0.999 probability that the elevator will notbe overloaded when it is filled with randomly selected clubmembers?
c. If the elevator is filled with 12 randomly selected clubmembers, what is the probability that the total load exceeds thesafe limit of 2100 lb? It his probability low enough?
d. What is the maximum number of passengers that should beallowed if we want a 0.999 probability that the elevator will notbe overloaded when it is filled with randomly selected clubmembers?

Explanation / Answer

c) x = 2100 / 12 =175lb P(X>175) = P(Z > (175-163)/(32/12) )                 = (Z > 1.299)                 = 1-0.9032                 = 0.0968 The probability is low, only 9.68% will over weight d)P(X > 2100/n) = 0.999    P(Z > (2100/n - 163)*n/32) = 0.999 According Z table, P(Z>3.08) = 0.999 (2100/n - 163)*n/32 = 3.08 n = 10.888 maximum people ˜10

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