The question asks for a test score that is 1.9 standard deviations below the mean for a normally distributed set of test scores.

Given:

• Mean ($\mu$) = 95
• Standard deviation ($\sigma$) = 15
• Distance from the mean = 1.9 standard deviations below

To calculate the test score:

$\text{Score} = \mu - (1.9 \times \sigma)$

Substituting the given values:

$\text{Score} = 95 - (1.9 \times 15)$ $\text{Score} = 95 - 28.5 = 66.5$

Thus, the test score that is 1.9 standard deviations below the mean is 66.5.

Would you like more details or have any other questions?

Here are 5 related questions to explore:

1. What is the test score 2.5 standard deviations above the mean?
2. How do you find the probability of scoring below a certain value in a normal distribution?
3. What percentage of scores falls between one standard deviation above and below the mean?
4. How do you standardize a score (convert to a z-score)?
5. If the standard deviation changes, how does it affect the spread of the distribution?

Tip: To calculate how far a value is from the mean, multiply the number of standard deviations by the standard deviation itself.