Questions: A positive z-score indicates that the data value is greater than the mean. below average less than greater than equal to

Solution Steps

To determine how a specific data value compares to the mean of a distribution, we calculate the z-score using the formula:

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

where:

• \( X = 75 \) (the data value),
• \( \mu = 70 \) (the mean),
• \( \sigma = 5 \) (the standard deviation).

Substituting the values into the formula gives:

\[ z = \frac{75 - 70}{5} = \frac{5}{5} = 1.0 \]

A positive z-score indicates that the data value is greater than the mean. In this case, since \( z = 1.0 \), it confirms that the value \( 75 \) is indeed greater than the mean \( 70 \).

Final Answer