# Thread: Getting standard deviation given probability

1. ## Getting standard deviation given probability

Hi all
If you have a mean of 2 and you want to get standard deviation with probability of 90% that the new mean will lie between 1.5 and 2.5. I tried to solve out this question by considering the inverse of Z score
Probability of 90% correspond to z =1.281 then I don't know how to solve out the following equation to get t0 (standard deviation)

Could you help me to solve this equation

2. ## Re: Getting standard deviation given probability

I don't follow your question or what you are explicitly asking. If this is a problem for a book or course, can you post the original question.

Thanks

3. ## Re: Getting standard deviation given probability

This is a problem in a course and it is about Byesian analysis. The problem is asking about estimating a priori estimate in the population. The mean measurement in the population is around 2, and we will assume there is a 90% probability of it being between 1.5 and 2.5. So the priori estimate follow normal distribution with a mean of 2 and we need to estimate standard deviation

4. ## Re: Getting standard deviation given probability

Well if you didn't say "Bayesian", I might have had a guess.

5. ## Re: Getting standard deviation given probability

Ok so what you are saying - just to make sure we understand you - is that you have a population mean which i assume to be normally distributed where and is undecided but youre beliefs are that - not 1.2815 as in youre picture because how can the probability be more than 1? - anyway you want to use this information in order to decide which prior to use and therefore need to find the such that ?

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