Consider the lifetime of a laser in Example 4-26.

Solution 183E

Step1 of 4:

Let us consider a random variable X it presents the lifetime of a Laser. And it  follows lognormal distribution with parameters

Here our goal is:

a). We need to find the probability the lifetime is less than 1000 hours.

b). We need to find the probability the lifetime is less than 11,000 hours given that it is more than 10,000 hours.

c). We need to compare the answers to parts (a) and (b).

Step2 of 4:

a).

Suppose a random variable X follows lognormal distribution with parameters  Then, The cumulative distribution of lognormal distribution is:

Now,

Where,is obtained from standard normal table(area under normal curve).

(In area under normal curve we have to see in row -2.0 under column 0.06)

Hence,