Solution
[tex]\begin{gathered} \text{Given} \\ \operatorname{mean},\text{ }\mu=5.2 \\ \text{standard deviation, }\sigma=2.4 \\ \\ \text{Recall the formula} \\ Z=\frac{x-\mu}{\sigma} \\ x-\mu=Z\sigma \\ x=Z\sigma+\mu \end{gathered}[/tex](a)
[tex]\begin{gathered} Z-\text{score for 95 percentile = 1.645} \\ x=Z\sigma+\mu \\ x=1.645(2.4)+5.2 \\ x=9.148 \\ x=9.15\text{ (2 decimal places)} \end{gathered}[/tex](b)
[tex]\begin{gathered} Z-\text{score for 60 percentile = }0.253 \\ x=Z\sigma+\mu \\ x=0.253(2.4)+5.2 \\ x=5.8072 \\ x=5.81\text{ (2 decimal places)} \end{gathered}[/tex](c)
[tex]\begin{gathered} Z-\text{score for first quartile (25\%) = }-0.674 \\ x=Z\sigma+\mu \\ x=-0.674(2.4)+5.2 \\ x=3.5824 \\ x=3.58\text{ (2 decimal places)} \end{gathered}[/tex]