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Stats: relative position

User XDiff
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1 Answer

2 votes

\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}

Alissa z score

x = 86.5 mean = 73.7 standard deviation = 8


\begin{gathered} z\text{ = }\frac{86^(\prime)5\text{ - 73.7}}{8} \\ =(12.8)/(8) \\ =\text{ 1.6} \end{gathered}

Emillo z score

x = 290.9 mean = 272 standard deviation = 21


\begin{gathered} z\text{ =}\frac{290.9\text{ - 272}}{21} \\ =\text{ }(18.9)/(21) \\ =\text{ 0.9} \end{gathered}

Frankie z score

x = 7.5 mean = 7.2 standard deviation = 0.6


\begin{gathered} z\text{ = }\frac{7.5\text{ - 7.2}}{0.6} \\ =\text{ }(0.3)/(0.6) \\ =\text{ 0.5} \end{gathered}

Final answer

From the normal distribution table

Alissa value = 0.4452

Emillo value

User CryptoJones
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4.1k points