Question

Assume you have a normal distribution with a mean of 51 and a standard deviation of 3. Find the value that gives you a z-score of -2.44. Round your answer to the nearest HUNDREDTH.

Answer 1

The formula for the z-score is given below as

`\begin{gathered} z=(x-\mu)/(\sigma) \\ where, \\ \mu=51 \\ \sigma=3 \\ z=-2.44 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} z=(x-\mu)/(\sigma) \\ -2.44=(x-51)/(3) \\ cross\text{ multiply, we will have} \\ x-51=3(-2.44) \\ x-51=-7.32 \\ collect\text{ similar terms, we will have} \\ x=-7.32+51 \\ x=43.68 \end{gathered}`

Hence,

The final answer is

`\Rightarrow43.68`