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I have a distribution of particle size, however I do not have the raw data, I only know about the bounds, approximately 33% of the data is less than 2 microns and about 0% is more than 45 microns, assuming that it is a normal distribution, is there any way to estimate that the median of this distribution is less or equal than 4 microns?

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    $\begingroup$ Your question seems unclear. What are you trying to estimate ? are you trying to estimate the probability that the median is $\leq$ 4 microns ? If it is a normal distribution, median is same as the mean. $\endgroup$ – rgk Jan 11 at 5:07
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Without the standard deviation, we cannot confirm the value of median/mean ( as both are the same in a normal distribution). I suggest what you can do with this situation is with present data you can perform hypothesis testing and make sure with how much confidence you can confirm mean as 4 microns. Anyway for this you again min amount of data for a sample at least. Basically, this question requires more data for a person who has no idea about the domain.

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