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 2.1 days.

What is the expected recovery time for the top 5% of patients?

How long was the recovery period for a patient with a z score of -1.3?

please show work

Answer 1

Solution:-

Given that,

mean = = 5.3

standard deviation = = 2.1

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.65) = 0.95  

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 2.1 + 5.3

x = 8.77

z = - 1.3

Using z-score formula,

x = z * +

x = - 1.3 * 2.1 + 5.3

x = 2.57