The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.8 days and a standard deviation of 2.5 days. what is the 85th percentile for recovery times? (round your answer to two decimal places.)

Mean: m=5.8 days
Standard deviation: s=2.5 days

85th percentile for recovery times: P(X<x)=85%=85/100→P(X<x)=0.85
x=?

P(X<x)=P(Z<z)=0.85
z=(x-m)/s

P(Z<z)=0.85
Using a normal distribution we get z=1.0364

Replacing in the equation of z:
z=(x-m)/s
1.0364=(x-5.8)/2.5

Solving for x:
1.0364(2.5)=x-5.8
2.591=x-5.8
2.591+5.8=x-5.8+5.8
x=8.391 days

Aswer: The 85th percentile for recovery times is 8.391 days