A ski boat has a maximum capacity of 6 people or 1050 pounds.  That capacity will be exceeded if 6 ...

A ski boat has a maximum capacity of 6 people or 1050 pounds.  That capacity will be exceeded if 6 people have weights with a mean of grater than 1050/6=175 pounds.  Because men tend to weigh more than women, a “worst case” scenario involves 6 male passengers.  Men’s weights are normally distributed with a mean of 182.9 pounds and a standard deviation of 40.8 pounds.  
 
 
a.   Find the probability that if an individual man is randomly selected, his weight will be          greater than 175 pounds.  Draw a sketch of this situation and round your probability to the nearest hundredths.  (6 points)
 
 
 
 
 
b.   Find the probability that 6 randomly selected men will have a mean that is greater          than 175 pounds. Draw a sketch of this situation and round your probability to the nearest hundredths.  



c.   Does the ski boat appear to have the correct weight limit?  Does part a or part b help
you decide this?  Justify your response.