The recovery time from a surgical procedure is normally distributed with a mean of 6.4 days and a standard deviation of 1.4 days. What is the z-score for a patient who takes 9 days to recover?

Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 6.4 days and a standard deviation of 1.4 days.

What is the z-score for a patient who takes 9 days to recover? (Round your answer to two decimal places.)

Answer 1

In a normal distribution, your z score represents how many standard deviations away from the mean the value of interest is. In this case, we want to know how many standard deviations 9 days is away from 6.4 days. In order to calculate this:

9 - 6.4 = 2.6

This means we are 2.6 days away. Since one standard deviation equals 1.4 days, and we want to know how many standard deviations are in 2.6, simply divide the numbers.

2.6 / 1.4 = 1.857142, which rounds to 1.86

z = 1.86