Question

A normal distribution has a mean of 111 and a standard deviation of 4. Find the z-score for a data value of 106. Round to two decimal places

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given values

`\begin{gathered} mean(\mu)=111 \\ std(\sigma)=4 \\ x=106 \end{gathered}`

STEP 2: Write the formula for calculating z score

`z=(x-\mu)/(\sigma)`

STEP 3: Find the z-score

`\begin{gathered} By\text{ substitution,} \\ x=(106-111)/(4)=(-5)/(4)=-1.25 \end{gathered}`

Hence, the z-score is -1.25