Question

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?

Answer 1

From the question, using the Zscore formula

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ x\text{ = sample mean = 44 and 64} \\ \mu=\text{ population mean = 54} \\ \sigma=\text{ standard deviation = 5} \end{gathered}`

For 44 we have

`\begin{gathered} Z=(44-54)/(5) \\ Z=(-10)/(5) \\ Z=-2 \end{gathered}`

For 64, we have

`\begin{gathered} Z=(64-54)/(5) \\ Z=(10)/(5) \\ Z=2 \end{gathered}`

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