Question

Corey has 4929 songs in his computer music library. The songs have a mean duration of 248.6 seconds with a standard deviation of 114.89 seconds. One of the songs is 363 seconds long. What is its z-score?

Answer 1

In order to calculate a z-score value, we need to use the following equation:

$Z=\frac{x-\mu}{\sigma}$

Where, x is the observed value,

μ is the mean, and

σ is the standard deviation of the sample

In this example,

$Z=\frac{363-248.6}{114.89}$

solving this, we obtain a Z-score of 0.9957