Quantitative Literacy Practice Exam 2025 – 400 Free Practice Questions to Pass the Exam

To determine the z-score for a data value, you can use the formula:

\[ z = \frac{(X - \mu)}{\sigma} \]

where \( X \) is the data value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.

In this case, the mean (\( \mu \)) is 104, the standard deviation (\( \sigma \)) is 5, and the data value (\( X \)) is 107.

Substituting the values into the formula:

\[ z = \frac{(107 - 104)}{5} \]

Calculating the numerator:

\[ 107 - 104 = 3 \]

Now substitute this back into the z-score formula:

\[ z = \frac{3}{5} = 0.6 \]

Thus, the z-score for the data value of 107 is 0.6. This indicates that the data value is 0.6 standard deviations above the mean. Understanding the concept of z-scores is important as they provide insight into how a specific data point compares to the overall distribution, allowing for standardized comparisons across different datasets.