A set of data items is normally distributed with a mean of 700 and a standard deviation of 10. Find the data item in this distribution that corresponds to the given \( z \)-score. \( z=-6 \) The data item that corresponds to \( z=-6 \) is \( \square \). (Type an integer or a decimal.)

To find the data item corresponding to a \( z \)-score, you can use the formula: \[ X = \mu + z \cdot \sigma \] Where \( X \) is the data item, \( \mu \) is the mean, \( z \) is the \( z \)-score, and \( \sigma \) is the standard deviation. Plugging in the values: - Mean (\( \mu \)) = 700 - Standard deviation (\( \sigma \)) = 10 - \( z \) = -6 So, \[ X = 700 + (-6) \cdot 10 \] \[ X = 700 - 60 \] \[ X = 640 \] The data item that corresponds to \( z=-6 \) is \( 640 \).