Question

Consider a set of data in which the sample mean is 23.8 and the sample standard deviation is 6.6. Calculate the z score given that x= 26.7 round your answer two decimal places.

Answer 1

SOLUTION

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

STEP 1: Write the given data

$\begin{gathered} mean(\mu)=23.8 \\ standard\text{ }deviation(\sigma)=6.6 \\ x=26.7 \end{gathered}$

STEP 2: Write the formula for calculating z-scores

$z=\frac{x-\mu}{\sigma}$

By substitution,

$\begin{gathered} z=\frac{26.7-23.8}{6.6}=\frac{2.9}{6.6}=0.43939393939 \\ \\ z\approx0.44 \end{gathered}$

Hence, the z score is approximately 0.44 to 2 decimal places