50 survival time after some treatment is 17 years the standa

50% survival time after some treatment is 1.7 years, the standart deviation is 0.4 How many patients out of 140 will survive after 5 years?

Note: log of survival time is distributed normally with the mean, equal to the natural log from 50% survival time and provided standart deviation. The distribution of the survival time itself is log-normal.

Solution

MEAN = 1.7

STD DEV = 0.4

P(X>5) =

For x = 5, z = (5 - 1.7) / 0.4 = 8.25

Hence P(x > 5) = P(z > 8.25) = [total area] - [area to the left of 2.25]

= 1 - 0.9878 = 0.0122 = 1.2%

1.2% OF 140 = 1.68 = 2 ROUND VALUE