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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!

Respuesta :

Hey there mate :)

Analysis :

[tex]401 = 515 - 114 = u - 6[/tex]

And

[tex]173 = 515 - 3.114 = u - 36[/tex]

[tex] = \frac{p(u - 36 < u < u + 36) - p(u - 6 < u < u + 6)}{2} [/tex]

[tex] = \frac{99.73percent - 68.21percent}{2} [/tex]

[tex] = \frac{31.46percent}{2} [/tex]

[tex] = {15.73percent}[/tex]

Then, calculating,

[tex]u - 26 = 515 - 2 \times 114 = 287[/tex]

And

[tex]u + 26 = 515 + 2 \times 114 = 743[/tex]

Then,

[tex]The \: Range = (287,743)[/tex]

Final Answers :-

15.73 %

(287,743)

~Benjemin360

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