Question

Consider a set of data and which a sample mean is 34.4 and the sample standard deviation is 3.7 calculate the Z score given that x=35.8. round answer to two decimal places

Answer 1

Explanation:

Step 1. The given information that we have about the data set is:

$\begin{gathered} Mean: \\ \mu=34.4 \end{gathered}$$\begin{gathered} Standard\text{ deviation:} \\ \sigma=3.7 \end{gathered}$$\begin{gathered} x-value: \\ x=35.8 \end{gathered}$

Step 2. We need to calculate the z-score. To calculate it, we use the following formula:

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

Step 3. Substituting the known values:

$z=\frac{35.8-34.4}{3.7}$

Step 4. Solving the operations:

$\begin{gathered} z=\frac{1.4}{3.7} \\ \downarrow \\ \boxed{z=0.3784} \end{gathered}$

Rounding the answer to two decimal places:

$\boxed{z=0.38}$

Answer:

$0.38$