Question

Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 20% of wait times?

Answer 1

solution

waiting times follow a normal distribution with

$$Mean, \mu=38.12$$ $$Standard\ deviation,\sigma=8.63$$

Longer waiting times are worse than shorter waiting times. Hence the worst 20% of wait times are wait times on the right tail of the distribution. The inferred level of confidence is 0.80.

The z value corresponding to the right tail probability of 0.2 is

$$Z=0.85$$

But

$$Z = \frac{x-\mu}{\sigma}$$ $$x =Z*\sigma +\mu$$ $$=0.85 * 8.63 +38.12 =45.4555$$

answer:

the shortest wait time that would still be in the worst 20% of wait times is 45.4555 minutes