A percentile rank of 40.9% corresponds to 0.409 in the above table which corresponds to a z-score of -0.23.
The z-score is computed as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where x is the observed value, μ is the mean and σ is the standard deviation.
In this case, the variance is 16, then the standard deviation is √16 = 4
Substituting into the z-score formula with z = -0.23, μ = 37, and σ = 4, we get:
[tex]\begin{gathered} -0.23=\frac{x-37}{4} \\ (-0.23)\cdot4=x-37 \\ -0.92+37=x \\ 36.08=x \end{gathered}[/tex]
