(1) Ski Gondola Safety. A ski gondola in Vail, Colorado, carries skiers to the t

Question

(1) Ski Gondola Safety. A ski gondola in Vail, Colorado, carries skiers to the top of a

mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 pounds.

Because men tend to weigh more than women, a ”worst case” scenario involves 12 passengers

who are all men. Men have weights that are normally distributed with a mean of 172lb and

a standard deviation of 29lb (based on data from the National Health Survey). Find the

probability that 12 randomly selected men will have a mean that is greater than 167 pounds

(so that their total weight is greater than the gondola maximum of 2004lb).

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    167      
u = mean =    172      
n = sample size =    12      
s = standard deviation =    29      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.597258899      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.597258899   ) =    0.72483273 [ANSWER]

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