If [tex]X[/tex] is a random variable representing test scores, then the 41st percentile is the score [tex]x[/tex] such that [tex]P(X\le x)=0.41[/tex]. Transform [tex]X[/tex] to the random variable [tex]Z[/tex] that follows the standard normal distribution via [tex]X=31.5+7.3Z[/tex]:
[tex]P(X\le x)=P\left(\dfrac{X-31.5}{7.3}\le\dfrac{x-31.5}{7.3}\right)=P\left(Z\le\dfrac{x-31.5}{7.3}\right)=0.41[/tex]
The [tex]z[/tex]-score for the 41st percentile is about -0.2275, so
[tex]\dfrac{x-31.5}{7.3}\approx-0.2275\implies\boxed{x\approx29.8}[/tex]
