Question

SAT scores normal distributed mean 985 and standard deviation of 169. AMT scores are normally distributed with a mean of 24.6 and a standard deviation of 3.5. It is assumed that the two tests measure thw same aptitude bit use different scales.

a). if a student is 46-percentile in SAT, find the actual SAT score.

b). what would be the equivalent AMT score?

c). if a student gets SAT score of 1220, find the equivalent AMT score.

Answer 1

Solution,

For SAT scores , the Normal distribution with,

   = 985 and   = 169

For AMT scores , the Normal distribution with,

   = 24.6 and   = 3.5

a) For 46th percentile , P(Z < z) = 46% = 0.46

But from z table , P(Z < -0.10) = 0.46

So , z = -0.10

Using z score formula,

x = + (z * )

= 985 + (-0.10 * 169)

= 968.1  

if a student is 46-percentile in SAT, the actual SAT score is 968.1

b) For AMT scores, the equivalent score is given by

x =   + (z * )

= 24.6 + (-0.10 * 3.5)

= 24.25

c) if a student gets SAT score of 1220 , then its z score is

z = (x - )/ = (1220 - 985)/169 = 1.39

the equivalent AMT score is given by,

x =   + (z * )

= 24.6 + (1.39* 3.5)

= 29.47