A set of data items is normally distributed with a mean of 60 and a standard deviation of 12. Convert the data item 48 to a z-score.
a
-1
b
-12
c
12
d
1
To convert a data item to a z-score, you need to use the formula:
z = (x - µ) / σ
where:
- z is the z-score
- x is the data item
- µ is the mean
- σ is the standard deviation
In this case, the data item is 48, the mean is 60, and the standard deviation is 12. Plugging the values into the formula:
z = (48 - 60) / 12
Simplifying the equation gives:
z = -12 / 12
z = -1
Therefore, the z-score for the data item 48 is -1. So, the correct answer is option a.