An airplane with 100 seats has a total baggage limit of 6000

An airplane with 100 seats has a total baggage limit of 6000 lbs (an average limit of 60 lbs per person). Suppose the total weight of the baggage checked by an individual passenger is a random variable x with a mean of 50 lbs and a standard deviation of 20 lbs.

1. What is the probability that the total weight of the bags of 100 passengers will exceed the limit? In other words, what is the probability that the mean baggage weight will exceed 60 lbs?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    60      
u = mean =    50      
n = sample size =    100      
s = standard deviation =    20      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    5      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   5   ) =    0.000000286652 [ANSWER]