The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4 days and a standard deviation of 2 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median recovery time?days

c. What is the Z-score for a patient that took 6 days to recover?

d. What is the probability of spending more than 4.2 days in recovery?

e. What is the probability of spending between 3.7 and 4.5 days in recovery?

f. The 85th percentile for recovery times isdays.