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

$\begin{gathered} Z_1=\frac{X-\mu}{\sigma} \\ =\frac{42-50}{8} \\ =\frac{-8}{8}=-1 \end{gathered}$

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

$\begin{gathered} Z_2=\frac{X-\mu}{\sigma} \\ =\frac{58-50}{8} \\ =\frac{8}{8}=1 \end{gathered}$

Hence, from the normal distribution graph

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