Question

An elevator has a placard stating that the maximum capacity is 1872 lbs long dash 12 passengers.​ So, 12 adult male passengers can have a mean weight of up to 1872 divided by 12 equals 156 pounds. If the elevator is loaded with 12 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 156 lb.​ (Assume that weights of males are normally distributed with a mean of 161 lb and a standard deviation of 27 lb​.) Does this elevator appear to be​ safe? The probability the elevator is overloaded is ?

​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that,

mean = = 161 lb

standard deviation = = 27 lb

n = 12

= = 161 lb

= / n = 27 / 12 = 7.79

P( > 156 lb) = 1 - P( < 156)

= 1 - P[( - ) / < (156 - 161) / 7.79]

= 1 - P(z < - 0.64)

Using z table,    

= 1 - 0.2611

= 0.7389

No, there is a good chance that 12 randomly selected people will exceed the elevator capacity.