My Math Forum  

Go Back   My Math Forum > High School Math Forum > Probability and Statistics

Probability and Statistics Basic Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 2nd, 2017, 04:45 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.
redsaints2010 is offline  
 
April 2nd, 2017, 05:13 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 1,646
Thanks: 836

Quote:
Originally Posted by redsaints2010 View Post
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)
romsek is online now  
Reply

  My Math Forum > High School Math Forum > Probability and Statistics

Tags
question



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
I have a question about sine and cosine transform, and the question also includes a H sCoRPion Differential Equations 0 March 16th, 2015 02:05 PM
Stats question: The Secretary Question word problem pudro Algebra 0 November 10th, 2008 09:12 PM





Copyright © 2017 My Math Forum. All rights reserved.