Question

The tensile strength Y of a certain material is such that Y= $e^{^{x}}$ where X is normally distributed with a mean of $\mu$ =10 and a variance of $\sigma ^{2}$ =1 (Y is said to follow a log-normal distribution. Compute each of the following:

a. P(Y<7,000) [hint: (lnY- $\mu$ )/ $\sigma$ ~N(0,1)]

b. P(10,000<Y<20,000)

c. P(Y>15,000)

Answer 1

a. P(Y<7,000)

In(y) _ μ P( ' In(7000) _ 10

b. P(10,000<Y<20,000)

$= P(\frac{ln(10000)-10}{1} < \frac{ln(Y) - \mu}{\sigma} < \frac{ln(20000)-10}{1})$

c. P(Y>15,000)

$= P(\frac{ln(Y) - \mu}{\sigma} > \frac{ln(15000)-10}{1})$