With the help of the 68-95-99 rule (see picture above) we know that those values with a z-score less than -2 are located in the 2.5% zone on the left.
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.
Substituting with z = -2, μ = 30, and σ = 10, we get:
[tex]\begin{gathered} -2=\frac{x-30}{10} \\ (-2)\cdot10=x-30 \\ -20+30=x \\ 10=x \end{gathered}[/tex]It is expected that 2.5% of the students spend less than 10 minutes.
