My question comes when I revise the topic. If the mean and simple information is given, how can I find the standard deviation? i.e. For normally distributed data, let's say mean = 65, and only 5 % or the samples are >=90. How can I find the standard deviation within so lack of information. Is it possible? Thanks to anyone who can suggest and share your idea.
2026-04-02 07:53:09.1775116389
Standard Deviation in Normal Distribution (with only mean and unknown division)
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Hint:
$\Phi^{-1}(0.95)\approx 1.644854$ for a standard normal distribution
so $5\%$ of a normal distribution is more than about $1.644854$ standard deviations above the mean
and you know the mean