Question

Assume you have a normal distribution with a mean of 64 and a standard deviation of 5. Find the Z-Score of 65, rounding your answer to the nearest HUNDREDTH.

Answer 1

0.2

Explanation:

The z-score formula is given below:

`z=(X-\mu)/(\sigma)\text{ where }\begin{cases}{X=Raw\text{ Score}} \\ {\mu=Mean} \\ {\sigma=Standard\;Deviation}\end{cases}`

Given a normal distribution with the given values below:

• Mean = 64

,

• Standard Deviation = 5

,

• Raw Score = 65

Substitute these values into the formula above:

`\begin{gathered} z-score=(65-64)/(5) \\ =(1)/(5) \\ =0.2 \end{gathered}`

The z-score is 0.2