Men have weights that are normally distributed with a mean of 172 lbs and a standard deviation of 29 lbs.  What is the probability that 12 randomly selected men will have a mean weight greater than 167 lbs?

College Algebra
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ISBN:9781337282291
Author:Ron Larson
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Chapter8: Sequences, Series,and Probability
Section8.7: Probability
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How to combine the probabilities of individual events to get the probability of several events occurring together, ie:

Men have weights that are normally distributed with a mean of 172 lbs and a standard deviation of 29 lbs.  What is the probability that 12 randomly selected men will have a mean weight greater than 167 lbs?

A.  I used the Rossman/Chance Normal Probability Calculator to determine that the probability of a randomly selected, individual man's weight being above 167 lbs. is 0.5684.  So for 12 men would I just raise 0.5684 to the 12th power? --> 0.5684^12 = 0.00114? 

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