11. Elevator Safety Example 2 referred to an Ohio elevator with a maximum capaci

Question

11. Elevator Safety Example 2 referred to an Ohio elevator with a maximum capacity of 2500 lb. When rating elevators, it is common to use a 25% safety factor, so the elevator should actually be able to carry a load that is 25% greater than the stated limit. The maximum capacity of 2500 lb becomes 3125 lb after it is increased by 25%, so 16 male passengers can have a mean weight of up to 195.3 lb. If the elevator is loaded with 16 male passengers, find the probability that it is overloaded because they have a mean weight greater than 195.3 lb. (As in Example 2, assume that weights of males are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb.) Does this elevator appear to be safe?

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =40.8/(16)1/2 =10.2

hence probability of mean weight greater then 195.3 lb =P(X>195.3)=1-P(X<195.3)=1-P(Z<(195.3-182.9)/10.2)=

=1 -P(Z<1.2157)=1-0.8879 =0.1121

as probbaility of that happenning is conserably high; the elevator is not seems to be safe for carrying 16 people .

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