Respuesta :
Answer:
[tex]\begin{gathered} X=95,z=0.25 \\ X=80,z=-0.5 \\ X=98,z=0.4 \\ X=88,z=-0.1 \\ X=105,z=0.75 \\ X=76,z=-0.7 \end{gathered}[/tex]Explanation:
Given a sample with the following:
• Mean,M = 90
,• Standard deviation, s = 20
To find the z-score for each of the given X values, we use the formula below:
[tex]\begin{equation*} z-score=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}{X=Raw\;Score} \\ {\mu=mean} \\ {\sigma=Standard\;Deviation}\end{cases} \end{equation*}[/tex]The z-scores are calculated below:
[tex]\begin{gathered} \text{When X=95, }z=\frac{95-90}{20}=\frac{5}{20}=0.25 \\ \text{When X=80, }z=\frac{80-90}{20}=\frac{-10}{20}=-0.5 \\ \text{When X=98, }z=\frac{98-90}{20}=\frac{8}{20}=0.4 \end{gathered}[/tex][tex]\begin{gathered} \text{When X=88,}z=\frac{88-90}{20}=\frac{-2}{20}=-0.1 \\ \text{When X=105, }z=\frac{105-90}{20}=\frac{15}{20}=0.75 \\ \text{When X=76, }z=\frac{76-90}{20}=\frac{-14}{20}=-0.7 \end{gathered}[/tex]