To determine the z-value, we need to first calculate the standard error. We can do this using the formula from the above section:
$\mathrm{SE}\=\frac{30}{\sqrt{50}}$,
$\mathrm{SE}\=4.242$
We can now plug in our known values and the standard error to calculate the z-value:
$z\=\frac{x-\mu}{\mathrm{SE}}$
$z\=\frac{118-120}{4.242}$
$z\=-0.471$
Now we can look up the probability: $P\left(z<-0.471\right)$ on a probability table.
$P\left(z<-0.471\right)\=0.3192$
Since 0.3192 is greater than P = 0.05, we cannot reject the null hypothesis that the sample mean is significantly different than the metal disc population mean.