Question

Log normal distribution. Mortgage amount, measured in thousands of dollars, follows a log normal distribution with parameters 5.4 and 0.7. What is the probability that the mortgage amount exceeds 200 thousand dollars?

Answer 1

below are parameter

mean(ϴ)=		5.4000
std dev(ω)=		0.7000

for lognormal distribution z score =(ln(x)-ϴ)/ω

probability that the mortgage amount exceeds 200 thousand dollars:

probability =P(X>200)=1-P(X<200)=1-P(Z<(ln(200)-5.4)/0.7)=1-P(Z<-0.15)=0.5596