11. Elevato 2500 lb. When rating elevators, it is common to use a 25% safety fac

Question

11. Elevato 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 31251b 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? r Safety Example 2 referred to an Ohio elevator with a maximum capacity of

Explanation / Answer

here for 16 passenger std error =std deviation/(n)1/2 =40.8/(16)1/2 =10.2

hence probability that average weight exceed 195.3 =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

for above probability is higher then 0.05 level of unusual valuues ; therefore elevator does not appear to be safe.

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