The lifetime (in days) of a certain electronic component

Solution 1E

Step1 of 5:

Let us consider a random variable X it presents lifetime of an certain electronic components. And X follows lognormal distribution with mean  and standard deviation .

That is XN(1.2, 0.42)

Here our goal is:

a).We need to find mean lifetime.

b).We need to find the probability that a component lasts between three and six days.

c).We need to find the median lifetime.

d).We need to find the 90th percentile of the lifetimes.

Step2 of 5:

a).

The probability density function of lognormal distribution is given by

Where,

mean

standard deviation

Z = standard normal variable.

Now, the mean lifetime is given by

               =

               =

          =

           = 3.5966

Hence, E(X) = 3.5966