Suppose human weights are normally distributed with mean 175 and standard deviat

Question

Suppose human weights are normally distributed with mean 175 and standard deviation 36 pounds. A helicopter is evacuating people from a building surrounded by zombies, and this helicopter can fit 9 people and with a maximum weight of 1800 pounds, i.e., an average of 200 pounds per person. If 9 people are randomly chosen to be loaded on this helicopter, what is the probability that it can safely lift off (i.e., the average weight of a person in the helicopter is less than 200)?

keep answers in decimal form and round to THREE decimal places

Explanation / Answer

a)We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    200      
u = mean =    175      
n = sample size =    9      
s = standard deviation =    36      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.083333333      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   2.083333333   ) =    0.981389575 = 0.981 [ANSWER]

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