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The lifetime of a microprocessor is exponentially
Chapter 4, Problem 16SE(choose chapter or problem)
The lifetime of a microprocessor is exponentially distributed with mean 3000 hours.
a. What proportion of microprocessors will fail within 300 hours?
b. What proportion of microprocessors will function for more than 6000 hours?
c. A new microprocessor is installed alongside one that has been functioning for 1000 hours. Assume the two microprocessors function independently. What is the probability that the new one fails before the old one?
Questions & Answers
QUESTION:
The lifetime of a microprocessor is exponentially distributed with mean 3000 hours.
a. What proportion of microprocessors will fail within 300 hours?
b. What proportion of microprocessors will function for more than 6000 hours?
c. A new microprocessor is installed alongside one that has been functioning for 1000 hours. Assume the two microprocessors function independently. What is the probability that the new one fails before the old one?
ANSWER:
Step 1 of 4:
It is given that lifetime of a microprocessor is distributed as exponentially with mean 3000 hours.
Let X denotes the lifetime of the microprocessor.
It is given that mean of exponential distribution =3000
=
Thus,
X~Exponential()
The [probability density function of x is given by,
f(x)=
=