Questions: Fill in the blank. The represents the number of standard deviations an observation is from the mean.

Solution Steps

To determine how far an observation is from the mean in terms of standard deviations, use the concept of the z-score or standard score.

We are given:

• Observation (\(X\)) = 75
• Mean (\(\mu\)) = 70
• Standard Deviation (\(\sigma\)) = 5

The z-score formula is: \[ z = \frac{X - \mu}{\sigma} \]

Substitute \(X = 75\), \(\mu = 70\), and \(\sigma = 5\) into the formula: \[ z = \frac{75 - 70}{5} \]

Simplify the numerator: \[ 75 - 70 = 5 \] Then divide by the standard deviation: \[ z = \frac{5}{5} = 1.0 \]

Final Answer