Answer to Question #93578 in Statistics and Probability for Ruby

Question

A consultant determined that typist could complete a set of documents in 12 minutes with a standard deviation of 3.5 minutes. Based on experience, the distribution is approximately normal. What is the z-score if a certain employee took 14 minutes to complete the document?

Answer 1

Let X denotes the document completion time. Then $X$ has a normal distribution with $\mu=12$ and $\sigma=3.5:$

$X\sim N(12, 3.5^2)$

If $X\sim N(\mu, \sigma^2),$ then

$$Z={X-\mu \over \sigma}\sim N(0, 1)$$

What is the z-score if a certain employee took 14 minutes to complete the document

$$Z={14-12 \over 3.5}={4 \over 7}\approx0.57143$$