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?

Z = (score-mean)/SD

Insert values and calculate.

-1.36

To find the z-score for a value of 40 in a normal distribution, you can use the formula:

z = (x - μ) / σ

Where:
- z is the z-score
- x is the value
- μ is the mean
- σ is the standard deviation

In this case:
- x = 40
- μ = 45
- σ = 3.25

Plugging in the values:

z = (40 - 45) / 3.25

Calculating:

z = -5 / 3.25

z ≈ -1.54

Therefore, the z-score for a value of 40 is approximately -1.54.