My Math Forum Normal Distribution: Calculating Mean and Standard Deviation

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 January 30th, 2016, 09:44 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, 03:58 PM #2 Global Moderator   Joined: May 2007 Posts: 6,380 Thanks: 542 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, 05:09 AM #3 Newbie   Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0 workings so would I be right in saying?; 1.2816 = (15-mu) / sigma and -0.6449 = (4-mu) / sigma Then use simultaneous equations to solve for both?
 February 4th, 2016, 04:42 PM #4 Global Moderator   Joined: May 2007 Posts: 6,380 Thanks: 542 Assuming you constants are correct, this is the right idea.
 February 5th, 2016, 07:07 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, 02:14 PM   #6
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 Originally Posted by wahhdoe I'm happy with the 1.2816 but I'm not convinced that -0.6449 is the correct value
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, 02:37 AM #7 Newbie   Joined: Nov 2015 From: brighton, uk Posts: 7 Thanks: 0 got there! wicked!! thanks for your help!

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