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

Solution:

The formula for the z-score is given below as

$\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where, \\ \mu=51 \\ \sigma=3 \\ z=-2.44 \end{gathered}$

By substituting the values, we will have

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

Hence,

The final answer is

$\Rightarrow43.68$