Question

the mean of a set of data is 3.14 and its standard deviation is 4.76. find the z - score for a value of 13.92. round to two decimal places.
a. 2.26
b. 2.56
c. 2.49
d. 2.03

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 3.14$, $\sigma=4.76$, and $x = 13.92$.

Step3: Substitute values into formula

$z=\frac{13.92 - 3.14}{4.76}=\frac{10.78}{4.76}$.

Step4: Calculate the result

$\frac{10.78}{4.76}\approx2.26$.

Answer:

A. 2.26