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January 30th, 2016, 08:44 AM  #1 
Newbie Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0  Normal Distribution: Calculating Mean and Standard Deviation
Hi All, As usual have been driving myself mad with this question; The heights of seedlings are normally distributed. Given that 10% of the seedlings are taller than 15cm and 5% are shorter than 4cm, find the mean and standard deviation of the heights. Have been playing around getting lots of different answers. Any help would be much appreciated, Thanks. 
January 30th, 2016, 02:58 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,586 Thanks: 612 
It looks like you should start with a normal distribution table. Find the points corresponding to 10% and above (above mean) and 4% and below (below mean). Linear transform to your coordinates. Finally use same linear transformation on 0 and 1 of the table to get your mean and standard deviation (subtracting the mean).

February 4th, 2016, 04:09 AM  #3 
Newbie Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0  workings
so would I be right in saying?; 1.2816 = (15mu) / sigma and 0.6449 = (4mu) / sigma Then use simultaneous equations to solve for both? 
February 4th, 2016, 03:42 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,586 Thanks: 612 
Assuming you constants are correct, this is the right idea.

February 5th, 2016, 06:07 AM  #5 
Newbie Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0 
I'm happy with the 1.2816 but I'm not convinced that 0.6449 is the correct value

February 5th, 2016, 01:14 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,586 Thanks: 612  These should have been obtained from a normal distribution table. I looked it up. Your upper number is correct, but I got ~ 1.645 for the lower number. It looks like you left out the 1. Note: the 5% or lower must be larger in magnitude than the 10% or above.

February 10th, 2016, 01:37 AM  #7 
Newbie Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0 
got there! wicked!! thanks for your help! 

Tags 
calculating, deviation, distribution, normal, standard 
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