My Math Forum Obtaining lower and upper limit

 August 16th, 2017, 06:20 AM #1 Member   Joined: May 2015 From: Australia Posts: 61 Thanks: 7 Obtaining lower and upper limit Question: What are safe cholesterol levels? Measurements of cholesterol for males 20 to 29 years old are approximately Normally distributed with mean 4.6 mmol/L and standard deviation 0.93 mmol/L. In medical diagnosis, physicians often use reference limits for judging results as ‘normal’ or else requiring further investigation or treatment. These are typically the limits within which we would expect to find 95% of healthy people. Obtain the lower and upper limit for that range in the case of cholesterol for males 20 to 29 years old. According to your range, at what cholesterol levels would we suspect a health problem? My answer: 95% of values under curve lies within two standard deviations of mean. Lower limit: μ-(2 x σ) =4.6 – (2 x 0.93) =2.74 mmol/L Upper limit: μ+(2× σ) 4.6 + (2 x 0.93) = 6.46 mmol/L The lower limit is 2.74 mmol/L and the upper limit is 6.46 mmol/L for the range we expect to find 95% of healthy people. According to this range, we'd suspect a health problem for cholesterol levels below 2.74 mmol/L or above 6.46 mmol/L. Is that method of solving the problem correct? Thanks in advance
 August 16th, 2017, 10:25 AM #2 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित I get slightly different values: Lower limit: μ-(2 x σ) =4.6 – (1.96 x 0.93) =2.7772 mmol/L Upper limit: μ+(2× σ) 4.6 + (1.96 x 0.93) = 6.4228 mmol/L
 August 16th, 2017, 11:11 AM #3 Senior Member   Joined: Aug 2012 Posts: 1,709 Thanks: 458 Ah, lim soup.
 August 16th, 2017, 02:52 PM #4 Member   Joined: May 2015 From: Australia Posts: 61 Thanks: 7 Hi, im confused as to why you changed the 2 to 1.96. Lower limit: μ-(2 x σ) =4.6 – (1.96 x 0.93) =2.7772 mmol/L
August 16th, 2017, 08:27 PM   #5
Member

Joined: May 2015
From: Australia

Posts: 61
Thanks: 7

My solution for this question is based off of the image i just attached which basically says that 95% of values under curve lies within two standard deviations of mean.

This is why I wrote 2 x 0.93 throughout the solution. I'm not sure why we should use 1.96 x 0.93?

Lower limit:
μ-(2 x σ)
=4.6 – (2 x 0.93)
=2.74 mmol/L
Upper limit:
μ+(2× σ)
4.6 + (2 x 0.93)
= 6.46 mmol/L
Attached Images

 August 16th, 2017, 08:57 PM #6 Math Team     Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित The curve I referred suggested the value of 95% in between -1.96 to 1.96

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