Question

Let Y have the lognormal distribution with mean 82.5 and variance 146.00. Compute the following probabilities

P(80 < Y < 108)

Answer 1

Given,

= 82.5 , = sqrt ( 146)

We convert this to standard normal as

P(Y < y) = P( Z < ( y - ) / )

So .,

P(80 < Y < 108) = P(Y < 108) - P(Y < 80)

= P(Z < (108 - 82.5) / sqrt(146) ) - P(Z < (80 - 82.5) / sqrt(146) )

= P(Z < 2.11) - P(Z < -0.21)

= 0.9826 - 0.4168 (From Z table)

= 0.5658