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The lifetime of a semiconductor laser has a lognormal
Chapter 4, Problem 175E(choose chapter or problem)
Problem 175E
The lifetime of a semiconductor laser has a lognormal distribution, and it is known that the mean and standard deviation of lifetime are 10,000 and 20,000, respectively.
(a) Calculate the parameters of the lognormal distribution.
(b) Determine the probability that a lifetime exceeds 10,000 hours.
(c) Determine the lifetime that is exceeded by 90% of lasers.
Questions & Answers
QUESTION:
Problem 175E
The lifetime of a semiconductor laser has a lognormal distribution, and it is known that the mean and standard deviation of lifetime are 10,000 and 20,000, respectively.
(a) Calculate the parameters of the lognormal distribution.
(b) Determine the probability that a lifetime exceeds 10,000 hours.
(c) Determine the lifetime that is exceeded by 90% of lasers.
ANSWER:
Solution
Step 1 of 3
a) We have to find the parameters of a lognormal distribution
Let X be the lifetime of the semiconductor
Let W has a normal distribution with mean 10,000 and standard deviation 20,000
The parameters of a lognormal distribution are
The mean of lognormal distribution is
The variance of lognormal distribution is =(20000)2
Let and
Now substitute in above equations
Then
Now square on both the sides
Now
And
Now substitute in the above equation
Now from
Now from
And from
Hence the parameters of a lognormal distribution are