Answer to Question #316806 in Statistics and Probability for Tag

Question

The length of stay of patients at a certain hospital in Cavite is 3 days with a standard deviation of 1.5 days. If a patient is selected at random, what is the probability that he/she will stay in the hospital between 3 and 7 days?

Answer 1

We have a normal distribution, $\mu=3, \sigma=1.5.$

Let's convert it to the standard normal distribution, $z=\cfrac{x-\mu}{\sigma};$

$z_1=\cfrac{3-3}{1.5}=0, \\z_2=\cfrac{7-3}{1.5}=2.67,$

$P(3<X<7)=P(0<Z<2.67)=\\=P(Z<2.67)-P(Z<0)=$

$=0.9962-0.5=0.4962$ ​(from z-table)