A set of data items is normally distributed with a mean of 900 and a standard deviation of 30. Find the data item in this distribution that corresponds to the given \( z \)-score. \( z=-2.5 \) The data item that corresponds to \( z=-2.5 \) is (Type an integer or a decimal.)

To find the data item that corresponds to the given \( z \)-score of -2.5, you can use the formula: \[ X = \mu + (z \times \sigma) \] Where: - \( X \) is the data item we want to find, - \( \mu \) is the mean (which is 900), - \( z \) is the z-score (-2.5), - \( \sigma \) is the standard deviation (30). Substituting in the values: \[ X = 900 + (-2.5 \times 30) \] \[ X = 900 - 75 \] \[ X = 825 \] The data item that corresponds to \( z = -2.5 \) is **825**.