Question

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 1.8 days.

What is the 85th percentile for recovery times? (Round your answer to two decimal places.)

Answer 1

Let x be the 85th percentile for recovery times

Therefore, P(X < x) = 0.85

Let z be the z-score corresponding to x so, P(Z < z) = 0.85

The z value corresponding to P(Z < z) = 0.85 is approximatley 1.04 (Obtained using standard normal table. Screneshot below)

Now, z = (x-μ)/σ

Substituting μ = 5.3, σ = 1.8 and z = 1.04 we get,

1.04 = (x-5.3)/1.8

x = 5.3 + 1.04*1.8

x = 7.17

The 85th percentile for recovery times is 7.17 days