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A variable X has a normal distribution withmean 54 and standard deviation 5. Approximately whatpercentage of the observations will fall between 44 and64? I know to use the z score formula and I get -2 and 2. What do I do after that?

Sagot :

SOLUTION

From the question, using the Zscore formula

[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ x\text{ = sample mean = 44 and 64} \\ \mu=\text{ population mean = 54} \\ \sigma=\text{ standard deviation = 5} \end{gathered}[/tex]

For 44 we have

[tex]\begin{gathered} Z=\frac{44-54}{5} \\ Z=\frac{-10}{5} \\ Z=-2 \end{gathered}[/tex]

For 64, we have

[tex]\begin{gathered} Z=\frac{64-54}{5} \\ Z=\frac{10}{5} \\ Z=2 \end{gathered}[/tex]

Finding the Zscore for -2 and 2 using the Zscore calculator

That is

[tex]P\mleft(-2Hence the answer is answer is 95.45%

The pics below should help

View image AaziyahZ23331
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