Question

weight of men is normal distributed with mean of 185 lb and standard deviation of 39 lb. A water taxi that holds 30 passengers has a maximum capacity of 6000 lb. If taxi is fully loaded with men, what is the probability that it goes over the maximum capacity? Round to 4 decimal places.

Answer 1

average capacity for a man =6000/30 =200

for normal distribution z score =(X-μ)/σ
here mean=       μ=	185
std deviation   =σ=	39.0000
sample size       =n=	30
std error=σx̅=σ/√n=	7.1204

probability that it goes over the maximum capacity:

probability =

P(X>200)

=

P(Z>2.11)=

1-P(Z<2.11)=

1-0.9826=

0.0174

( please try 0.0176 if this comes wrong due to rounding)