The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.7 days and a standard deviation of 2.4 days. What is the 90th percentile for recovery times? (Round your answer to two decimal places.)

Answer: the 90th percentile for recovery times is 8.77 days.

Step-by-step explanation:

Let x be the random variable representing the recovery time of patients from a particular surgical procedure. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ) / σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 5.7 days

σ = 2.4 days

The probability for the 90th percentile is 90/100 = 0.9

The z score corresponding to the probability value on the normal distribution table is 1.28

Therefore,

1.28 = (x - 5.7) / 2.4

Cross multiplying, it becomes

1.28 * 2.4 = x - 5.7

3.072 = x - 5.7

x = 3.072 + 5.7 = 8.77 days