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April 2nd, 2017, 03:45 PM  #1 
Newbie Joined: Apr 2017 From: NC Posts: 5 Thanks: 0  Help with question
I need help setting up this question and understanding it. 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 greater 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. 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. 
April 2nd, 2017, 04:13 PM  #2  
Senior Member Joined: Sep 2015 From: CA Posts: 1,112 Thanks: 580  Quote:
weight is distributed $N(182.9, 40.8)$ $P[\text{weight }> 175~lb] = 1  P[\text{weight }\leq 175~lb] = 1\Phi\left(\dfrac{175182.9}{40.8}\right)$ and I leave you to complete it. The sketch is almost identical to the previous one, just the parameters have changed. Quote:
You can plug in all the numbers and evaluate the probability. Quote:
 

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