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 April 2nd, 2017, 03:45 PM #1 Newbie   Joined: Apr 2017 From: NC Posts: 8 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
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 Originally Posted by redsaints2010 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.
This is pretty much the same as the last problem.

weight is distributed $N(182.9, 40.8)$

$P[\text{weight }> 175~lb] = 1 - P[\text{weight }\leq 175~lb] = 1-\Phi\left(\dfrac{175-182.9}{40.8}\right)$

and I leave you to complete it.

The sketch is almost identical to the previous one, just the parameters have changed.

Quote:
 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.
The mean of normal random variables with mean $\mu$ and standard deviation $\sigma$ will be distributed as a normal random variable with mean $\mu$ and standard deviation $\dfrac{\sigma}{\sqrt{n}}$

You can plug in all the numbers and evaluate the probability.

Quote:
 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.
this should be pretty clear based on the answer to (b)

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