How do I find the median for this problem?

Question

"The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.1 days"

how do I find the median recovery time? (If you could help explain the steps it would be very helpful, thanks!)

Answer 1

Well the mean and the median are the same for Normal Distribution,

so 5.2

However, proceeding naively.....

THe z-score, z, is needed, such that Prob(Z<z) = 0.5

Reverse table lookup and outright reasoning says

that the z-score is z=0 (the left side of the bell curve)

X = z*stnddev + mean = 0*2.1+5.2 = 5.2 <-- see, told ya!

This holds in general, since the z-score is 0 for

the median (or 50th percentile)