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
