Let's find the correct z-score for the given values.
The formula you're using to calculate the z-score is correct:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Where:
- [tex]\( x \)[/tex] is the value we're comparing (1140 in this case)
- [tex]\( \mu \)[/tex] is the mean (1400 in this case)
- [tex]\( \sigma \)[/tex] is the standard deviation (130 in this case)
Let's plug in the numbers:
[tex]\[ z = \frac{1140 - 1400}{130} \][/tex]
Subtract the mean from the value [tex]\( x \)[/tex]:
[tex]\[ 1140 - 1400 = -260 \][/tex]
Then divide this result by the standard deviation:
[tex]\[ z = \frac{-260}{130} \][/tex]
Now perform the division:
[tex]\[ z = -2.0 \][/tex]
So, the z-score for the value \$1140 is:
[tex]\[ z = -2.0 \][/tex]
