'If 2 grp have different SD but same mean, how do I know their SD given their combined SD and mean?

Known that

entry IQ of a school is 138 (assume all eligible student will be accepted)
female has lower SD than male
the proportion of the school is 2/5 female, 3/5 male
IQ are normally distributed with mean 100 (all integers)
female and male are each 1/2 of total population.
If the overall SD of the population is 15, what's the estimated SD for male and female?

I tried to do a while loop to calculate, but my female SD was larger than male, guess my equation was wrong somewhere....

the dataset was generated using default_rng.normal

need help how to solve using python

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