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**

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