Need some help with finding exact percentile

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Hi!

I have information about the following percentiles of normal distribution of data: P5%, P10%, P50%, P90% and P97%.
For each index (day in my case) I know the value of each one of the percentiles above. For example, for day 6 I know that its P5% value is 40, P10% value is 55 and so on...
My question is how can I get the exact percentile of a given value?
For example, if I have the value 45, how do I know what percentile is it?
If the value was 40, I could say that the percentile is 5, if it was 55, I knew the percentile is 10, but my value is somewhere in the middle, so how do I know it?

Thanks !
Tom Rahav.
[email protected]

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Use the Z score
If you know two percentile values and that the distribution is normal, you can calculate the mean and standard deviation for the population it came from and from there, determine the percentile of any given value.

First, determine the Z score for the percentile values you know. You can do this in Excel using the NORMSINV function or look it up in a book of math tables.

Next, Z = (value - mean) / standard deviation. Since you know the values and the Z scores from the percentiles, with two data points, you can solve for the mean and standard deviation.

Lastly, calculate the new Z score using the formula above and the new value you want to know the percentile of. Look up that Z score in the math handbook or use the NORMSDIST function in Excel.

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Need some help with finding exact percentile

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