Question

A certain website averages 4.9 hours of downtime per month with a standard deviation of 0.5 hours. In April, it had 3.5 hours of downtime. What z-score does the 4.5 correspond to?

Answer 1

The z-score of an observation is a convenient way to compare different distributions to each other. The z-score is defined mathematically as
`(x-m)/(s)` where m is the mean and s is the standard deviation. Intuitively, this means that we account for how far off the center of the distribution this observation is, while simultaneously taking into account the spread of the distribution. Substituting x=3.5, m=4.9 and s=0.5, we get that z=-2.8. Negative z-scores imply observations below the mean.