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SAT scores normal distributed mean 985 and standard deviation of 169. AMT scores are normally distributed...

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.

Solutions

Expert Solution

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


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