Question

AN elevator has a placard stating that the maximum capacity is1720lb-10passengers. So , 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 172lb.(Assume that weights of males are normally distributed with mean of 177 lb and a standard deviation of32lb). Dose this elevator appear to be safe?

Answer 1

We will check if the elevator can hold 10 man
X~(177,32^2)
n= 10
P(SigmaX>172)
SigmaX~(177*10,(32^2)*10)
SigamX~N(1770, 101.19^2)
P(SigmaX>172*10=1720) =Z=(1720-1770)/101.19
Z = -0.49
From Z table Z=-0.49
P(Z=-0.49) = 0.3121 (probability they will not overload)
1- 0.3123 = 0.6879 = 68.79%
The elevator is not safe, the probability to be more the 172 is 68.79%, high probability they could not make it.