Assuming that the data are normally distributed with a mean of 45 and a standard deviation of 3.25, what is the z-score for a value of 40?
To find the z-score for a given value, you can use the formula:
z = (X - μ) / σ
where:
- z is the z-score,
- X is the given value,
- μ is the mean of the data, and
- σ is the standard deviation of the data.
In this case, the given value is X = 40, the mean is μ = 45, and the standard deviation is σ = 3.25.
Now, let's substitute these values into the formula:
z = (40 - 45) / 3.25
Calculating this expression:
z = -5 / 3.25
z ≈ -1.54
Therefore, the z-score for the value of 40 is approximately -1.54.