You have computed the z score for a value.Then you realize that the actual standard deviation of the population is 25% larger than the one you used for computing the z value.Your corrected z value will be _______.
A)25% smaller than the original value
B)25% larger than the original value
C)75% smaller than the original value
D)20% larger than the original value
E)20% smaller than the original value

Question

Quizplus · Accepted Answer

The z score is calculated as $z = \frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. If the actual standard deviation is 25% larger, the denominator in the z score calculation increases, making the z score smaller. A 25% increase in the denominator does not lead to a 25% decrease in the z score, but it does make the z score smaller. Among the given options, the one that correctly reflects a decrease in the z score due to an increase in the standard deviation is the option indicating the z score will be 20% smaller, as this option correctly captures the direction of change without specifying an exact proportional relationship.

You Have Computed the Z Score for a Value