Question

An elevator has a placard stating that the max capacity is 2028lb- 12 passengers. So, 12 adult males passengers can have mean weight up to 169lbs. If the elevator is loaded with 12 adult males, find the probability that it is overloaded because they have a mean weight greater than 169lb. Assume weight of males normally distributed with a mean of 175lb and standard deviation of 27lb. Does this elevator appear to be safe? How can I solve this using TI-83?

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	175
std deviation   =σ=	27.0000
sample size       =n=	12
std error=σx̅=σ/√n=	7.7942

probability that it is overloaded because they have a mean weight greater than 169lb :

probability =P(X>169)=P(Z>(169-175)/7.794)=P(Z>-0.77)=1-P(Z<-0.77)=1-0.2207=0.7793

(for ti-83: press 2nd-vars : normalcdf(169,10000,175,27) will give above value)