Question

find the z - score for the value 51, when the mean is 56 and the standard deviation is 5.
z = - 1
z = 0.90
z = - 0.90
z = - 1.33

Explanation:

Step1: Recall z - score formula

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

Step2: Substitute given values

We are given $x = 51$, $\mu=56$, and $\sigma = 5$. Substitute these into the formula: $z=\frac{51 - 56}{5}$.

Step3: Calculate the numerator

$51-56=-5$, so $z=\frac{-5}{5}$.

Step4: Calculate the z - score

$\frac{-5}{5}=-1$.

Answer:

A. $z=-1$