Question

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

Answer 1

Hey there mate :)

Analysis :

$401 = 515 - 114 = u - 6$

And

$173 = 515 - 3.114 = u - 36$

$= \frac{p(u - 36 < u < u + 36) - p(u - 6 < u < u + 6)}{2}$

$= \frac{99.73percent - 68.21percent}{2}$

$= \frac{31.46percent}{2}$

$= {15.73percent}$

Then, calculating,

$u - 26 = 515 - 2 \times 114 = 287$

And

$u + 26 = 515 + 2 \times 114 = 743$

Then,

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

Final Answers :-

15.73 %

(287,743)

~Benjemin360