Solving Forearm Length Stats Problem

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Discussion Overview

The discussion revolves around a statistics problem related to forearm length and height, specifically focusing on calculating percentages based on given averages and standard deviations. The scope includes mathematical reasoning and problem-solving in preparation for a test.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in solving the problem and seeks assistance, noting their calculation of 38% for the first part of the question.
  • Another participant questions the independence of forearm length and height, suggesting that the correlation must be considered in the calculations.
  • A third participant proposes that "r=0.80" refers to the correlation coefficient and discusses the probability around the mean for independent normal distributions, suggesting a percentage of 38.3%.
  • A later reply indicates that the original poster found a solution and confirms the correlation coefficient interpretation, stating that the answer is 60% as given in the book.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method of solving the problem, with differing views on the independence of the variables and the implications of the correlation coefficient.

Contextual Notes

There are unresolved assumptions regarding the relationship between forearm length and height, as well as the dependence on the correlation coefficient in the calculations.

pinksapphire168
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Hi Everyone,

I am new to the forum and really need so help before I have a test tomorrow. I have been going over my book and working through the problems but I am stuck on this problem. Would someone please help me? thank you very much for your time

From a study
average height of men =68in sd=2.7inch
average forearm length=18in sd 1inch r=0.80

a) what percentage of men have forearms which are 18 inches long to the nearest inch? for this problem I figured out 38%

b) of the men who are 68inches tall, what percentage have forearms which are 18 inches long to the nearest inch?

I know that the nearest inch refers to 17.5 and 18.5 and the answer in the back of the book is 60% however, I do not know how they solve the problem to get 60%
 
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Since I don't believe that "forearm length" and "height" are independent, I don't see any way to do this with knowing the correlation.
 
I wonder whether "r=0.80" in the OP stands for corr.

For indep. normal distributions, since sd = 1 for the forearm length, the question is, what is the probability around the mean plus/minus half a sd? You can look it up from a standard normal table (e.g. http://www.math.unb.ca/~knight/utility/NormTbl0.htm ). I believe 38.3%.

For correlated distributions you need to think about multivariate normal.
 
Last edited by a moderator:
found the answer

Thank you for the replies, I already found a way to solve the problem.

r stands for coefficient correlation
and the answer as I included is 60%
 

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