To find the z-score for William's exam grade, we can follow these steps:
1. Identify the given values:
- Mean (μ): 67
- Standard deviation (σ): 2.0
- William's score: 66
2. Understand the formula for the z-score:
The z-score is calculated using the formula:
[tex]\[
z = \frac{(X - \mu)}{\sigma}
\][/tex]
where:
- [tex]\( X \)[/tex] is the value of the score (William's score in this case).
- [tex]\( \mu \)[/tex] is the mean.
- [tex]\( \sigma \)[/tex] is the standard deviation.
3. Substitute the known values into the formula:
[tex]\[
z = \frac{(66 - 67)}{2.0}
\][/tex]
4. Perform the subtraction inside the parentheses:
[tex]\[
66 - 67 = -1
\][/tex]
5. Divide the result by the standard deviation:
[tex]\[
z = \frac{-1}{2.0} = -0.5
\][/tex]
6. Round the z-score to two decimal places:
[tex]\[
z = -0.50
\][/tex]
Thus, the z-score for William's exam grade is -0.50 after rounding to two decimal places.
