Question

The distribution of SAT scores is approximately normal with a mean of 1500.

If 1628 is the 90th percentile, what is the standard deviation?

Answer 1

Hello,

Answer

`\sigma=457,95...`

Explanation:

p(z<a)=0.9

p(z<1.29)=0.9015

p(z<1.28)=0.8997

using linear interpolation: with 4 decimals

p(z<1.282)<0.9

`(1628-1500)/(\sigma) =1.282\\\\\sigma =(1628-1500)/(1.282)\\\\\sigma=457,95...\\`