The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.9 days and a standard deviation of 2.1 days. what is the 85th percentile for recovery times?

The 85th percentile is the cutoff time such that



In other words, the 85th percentile refers to the time needed to belong to the top 15% of the distribution; more generally, the percentile is the top of the distribution.

Anyway, to find this value of , transform to a random variable with the standard normal distribution using



where is the mean of and is the standard deviation of .



Here is used to denote the z-score corresponding to the cutoff time . Referring to a z-score table, you find that this occurs for . So,