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

Step-by-step 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=(x-\mu)/(\sigma)`

Step 3. Substituting the known values:

`z=(35.8-34.4)/(3.7)`

Step 4. Solving the operations:

`\begin{gathered} z=(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`