Question

4) In the 2014–2015 academic year, 1,108,165 high school seniors took the SAT. That year the mean of the scores from the math portion was 501 with a standard deviation of 117. What percentage scored between 600 and 700 points? Round to the second decimal place (0.12).

5) In the 2014–2015 academic year, 1,108,165 high school seniors took the SAT. That year the mean of the scores from the math portion was 501 with a standard deviation of 117. If a student’s score is 725, what is their percentile rank? Round to the second decimal place (0.12).

Answer 1

4) µ = 501, σ = 117

P(600 < X < 700) =

= P( (600-501)/117 < (X-µ)/σ < (700-501)/117 )

= P(0.8462 < z < 1.7009)

= P(z < 1.7009) - P(z < 0.8462)

Using excel function:

= NORM.S.DIST(1.7009, 1) - NORM.S.DIST(0.8462, 1)

= 0.1542 = 15.42%

5)

P(X = 725) =

= P( (X-µ)/σ = (725-501)/117 )

= P(z = 1.9145)

Using excel function:

= NORM.S.DIST(1.9145, 1)

= 0.9722 = 97.22%