# I want to apply to a university where the 25th /75th percentiles for the SAT Math are 490 / 620 respectively, but I am curious how would I find the mean and the standard deviation assuming that the data is normally distributed? I know that we are talking about the middle 50th-percentile and z_0.25=620 and z_0.75=490

I want to apply to a university where the 25th /75th percentiles for the SAT Math are 490 / 620 respectively, but I am curious how would I find the mean and the standard deviation assuming that the data is normally distributed? I know that we are talking about the middle 50th-percentile and ${z}_{0.25}=620$ and ${z}_{0.75}=490$
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If you want an EXCEL Solution, here it is:
The two equations are:
$\frac{490-\mu }{\sigma }$ = Normsinv(.25) = -0.67449
$\frac{620-\mu }{\sigma }$ = Normsinv(.75) = 0.67449
Solve for $\mu$ and $\sigma$