Question

Scores by women on the SAT-1 test are normally distributed with a mean of 988 and a standard deviation of 202. Scores by women on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.6.

If a women gets a SAT score that is the 77th percentile, find her actual SAT score and her equivalent ACT score.

Answer 1

For SAT ,

X ~ N ( µ = 988 , σ = 202 )
P ( X < x ) = 77% = 0.77
To find the value of x
Looking for the probability 0.77 in standard normal table to calculate critical value Z = 0.7388
Z = ( X - µ ) / σ
0.7388 = ( X - 988 ) / 202
X = 1137.24

X = 1137

For ACT

X ~ N ( µ = 20.9 , σ = 4.6 )
P ( X < x ) = 77% = 0.77
To find the value of x
Looking for the probability 0.77 in standard normal table to calculate critical value Z = 0.7388
Z = ( X - µ ) / σ
0.7388 = ( X - 20.9 ) / 4.6
X = 24.30

X = 24