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.)

Question

Fatima Valentine

Mathematics

20 April, 17:57

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.)

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Chace Mckay · Answer 1

Mean: m=5.8 days

Standard deviation: s=2.5 days

85th percentile for recovery times: P (X
x=?

P (X
z = (x-m) / s

P (Z
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: T he 85th percentile for recovery times is 8.391 days