Question

A set of data has a normal distribution With a mean of 50 And a standard deviation of 8. What percentage should fall between 42-58?

Answer 1

Given the following data:

`\begin{gathered} \text{mean(}\mu)=50 \\ \text{ standard deviation(}\sigma)=8 \end{gathered}`

Step 1: Find the Z-score for X= 42

`\begin{gathered} Z_1=(X-\mu)/(\sigma) \\ =(42-50)/(8) \\ =(-8)/(8)=-1 \end{gathered}`

Step 2: Find the Z-score for X = 58

`\begin{gathered} Z_2=(X-\mu)/(\sigma) \\ =(58-50)/(8) \\ =(8)/(8)=1 \end{gathered}`

Hence, from the normal distribution graph

[tex]\begin{gathered} P(-1Therefore, the percentage that should fall between 42-58 is 68%