Question

The records of a certain hospital showed that the length of stay of its patients is normally distributed with a mean of 11.5 days and a standard deviation of 2 days. Find the standard score that corresponds to a hospital stay of 9 days.

Answer 1

Let $X=$ the length of stay: $X\sim N(\mu, \sigma^2)$

$$z=\dfrac{x-\mu}{\sigma}=\dfrac{9-11.5}{2}=-1.25$$