Respuesta :
Solution
- In order to solve the question, we need to know the formula below:
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ where, \\ Z=\text{ The Z-score} \\ X=\text{ The individual score} \\ \mu=\text{ The mean score} \\ \sigma=\text{ The standard deviation} \end{gathered}[/tex]- The question has given us the following parameters:
[tex]\begin{gathered} \mu=73 \\ \sigma=8 \end{gathered}[/tex]- With the above information, we can proceed to solve the question as follows:
Question A:
[tex]\begin{gathered} X=73 \\ \therefore Z=\frac{73-73}{8}=\frac{0}{8} \\ \\ Z=0 \end{gathered}[/tex]Question B:
[tex]\begin{gathered} X=83 \\ \therefore Z=\frac{83-73}{8}=\frac{10}{8} \\ \\ Z=\frac{5}{4} \end{gathered}[/tex]Question C:
[tex]\begin{gathered} X=63 \\ Z=\frac{63-73}{8}=-\frac{10}{8} \\ \\ Z=-\frac{5}{4} \end{gathered}[/tex]Question D:
[tex]\begin{gathered} Z=-2.5 \\ \therefore-2.5=\frac{X-73}{8} \\ Cross\text{ multiply,} \\ 8(-2.5)=X-73 \\ Add\text{ 73 to both sides} \\ X=73+8(-2.5) \\ X=53 \end{gathered}[/tex]Question E:
[tex]\begin{gathered} Z=1.5 \\ 1.5=\frac{X-73}{8} \\ Cross\text{ Multiply,} \\ 1.5(8)=X-73 \\ Add\text{ 73 to both sides} \\ X=1.5(8)+73 \\ X=85 \end{gathered}[/tex]Question F:
[tex]\begin{gathered} Z=1.77 \\ 1.77=\frac{X-73}{8} \\ Cross\text{ Multiply,} \\ 8(1.77)=X-73 \\ Add\text{ 73 to both sides} \\ X=73+8(1.77) \\ \therefore X=87.16 \end{gathered}[/tex]