Answer :
Solution
Given
[tex]\begin{gathered} \text{ mean }\mu=17 \\ \\ \text{ standard deviation }\sigma=7 \end{gathered}[/tex]The Z score is given by the formula;
[tex]Z=\frac{X-\mu}{\sigma}[/tex](a)
[tex]Z=\frac{20-17}{7}\approx0.43\text{ \lparen nearest hundredth\rparen}[/tex](b)
[tex]Z=\frac{15-17}{7}\approx-0.29\text{ \lparen nearest hundredth\rparen}[/tex](c)
when Z = 1
[tex]\begin{gathered} \Rightarrow1=\frac{X-17}{7} \\ \\ \Rightarrow7=X-17 \\ \\ \Rightarrow X=7+17 \\ \\ \Rightarrow X=24 \end{gathered}[/tex]when Z = -0.1
[tex]\begin{gathered} \Rightarrow-0.1=\frac{X-17}{7} \\ \\ \Rightarrow-\frac{7}{10}=X-17 \\ \\ \Rightarrow X=17-\frac{7}{10} \\ \\ \Rightarrow X=16.3 \end{gathered}[/tex]When Z = 0
[tex]\begin{gathered} \Rightarrow0=\frac{X-17}{7} \\ \\ \Rightarrow0=X-17 \\ \\ \Rightarrow X=17 \end{gathered}[/tex]