Question

SAT math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114.

What percentage of SAT scores is between 173 and 401?

Find the SAT Math score range that falls with 2 standard deviations.

Please explain!

Answer 1

Hey there mate :)

Analysis :

`401 = 515 - 114 = u - 6`

And

`173 = 515 - 3.114 = u - 36`

`= (p(u - 36 < u < u + 36) - p(u - 6 < u < u + 6))/(2)`

`= (99.73percent - 68.21percent)/(2)`

`= (31.46percent)/(2)`

`= {15.73percent}`

Then, calculating,

`u - 26 = 515 - 2 * 114 = 287`

And

`u + 26 = 515 + 2 * 114 = 743`

Then,

`The \: Range = (287,743)`

Final Answers :-

15.73 %

(287,743)

~Benjemin360