3. \( \mu=18.4 ; \sigma=5 \); three standard deviations below the mean

To find the value that is three standard deviations below the mean, you can use the formula: \( \text{Value} = \mu - 3\sigma \). Plugging in your values, it would be \( 18.4 - 3 \times 5 = 18.4 - 15 = 3.4 \). So, three standard deviations below the mean is 3.4. Understanding standard deviations offers insights into how spread out your data points are. If you visualize a normal distribution curve, three standard deviations below the mean captures the "tail end" of the curve, indicating that values below 3.4 are relatively rare in your dataset.