A set of data items is normally distributed with a mean of 50 and a standard deviation of 4 . Convert 40 to a z-score. \( z_{40}=\square \) (Type an integer or a decimal.)

To convert a data point to a z-score, we use the formula: \[ z = \frac{x - \mu}{\sigma} \] where: - \( z \) is the z-score, - \( x \) is the value to be converted (in this case, 40), - \( \mu \) is the mean (50), and - \( \sigma \) is the standard deviation (4). Now, let's substitute the known values into the formula: \[ z_{40} = \frac{40 - 50}{4} \] Now, we will perform the calculation step by step: 1. Calculate \( 40 - 50 \): \[ 40 - 50 = -10 \] 2. Now divide by the standard deviation (4): \[ z_{40} = \frac{-10}{4} = -2.5 \] Thus, the z-score for 40 is: \[ z_{40} = -2.5 \]