Question

The number of homes sold each year by a realtor is normally distributed with a mean of 54. If the realtor sold 36 homes last year with a z-score of -2.4, what is the standard deviation? I

Answer 1

7.5

Step-by-step explanation:

Given the following:

`\begin{gathered} Z-\text{Score}=-2.4 \\ \text{Mean,}\mu=54 \\ X-\text{Value}=36 \end{gathered}`

Substitute these into the formula for Z-Score:

`Z-\text{Score}=(X-\mu)/(\sigma)\text{ where }\sigma=\text{standard deviation}`

This gives:

`\begin{gathered} -2.4=(36-54)/(\sigma) \\ -2.4=(-18)/(\sigma) \\ -2.4\sigma=-18 \\ \sigma=(-18)/(-2.4) \\ \sigma=7.5 \end{gathered}`

The standard deviation is 7.5