The lifetime of a microprocessor is exponentially distributed with a variance of 4,000,000 hours. a. What...

Question

Question

The lifetime of a microprocessor is exponentially distributed with a variance of 4,000,000 hours.

a. What proportion of microprocessors will function for less than 5,000 hours?

b. A microprocessor has been functioning for 1,000 hours. What is the probability that it will

function for a total of at least 6,000 hours?

Answer 1

Answer #1

Ans:

a)

mean=sqrt(4000000)=2000

P(T<=5000)=1-exp(-5000/2000)=0.9179

b)

P(T>=6000/T>=1000)=P(T>=5000)

=exp(-5000/2000)=0.0821

Answer 2

Similar Homework Help Questions

Suppose hard drive A has a lifetime that is exponentially distributed with mean of 7 years...

Suppose hard drive A has a lifetime that is exponentially distributed with mean of 7 years and hard drive B has a lifetime that is exponentially distributed with a mean of 4 years. What is the probability that drive B lasts at least 6 times longer than drive A?
The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What...

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours? .6321 .5507 .7135 .4493
The lifetime of a refrigerator (measured in years) is exponentially distributed with the expected lifetime equal...

The lifetime of a refrigerator (measured in years) is exponentially distributed with the expected lifetime equal to 17. What is the probability IN PERCENTAGES that the refrigerator will last more than 19?

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What...

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last more than 1,200 hours? A .3012 B .4345 C .3679 D .6988
The life of a lightbulb is distributed normally the variance of a lifetime is 625 and...

The life of a lightbulb is distributed normally the variance of a lifetime is 625 and the mean lifetime of a bulb is 530 hours find the probability of a bulb lasting for at least 480 hours
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model...

2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...

1. The time to failure of a digital camera (in hours) is distributed exponentially with parameter...

1. The time to failure of a digital camera (in hours) is distributed exponentially with parameter 10^−4 . a) Find the expected time to failure. (5) b) Find the probability that the camera will last less than 9,000 hours or more than 12,000 hours. (10) c) Find the probability that the camera will last more than 10,000 hours. (10) d) If the camera has lasted 10,000 hours, find the probability that it will last another 10,000 hours or longer. (10...
Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ (lambda) = 0.5

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ (lambda) = 0.5.What's the probability that a repair takes less than 5 hours? AND what's the conditional probability that a repair takes at least 11 hours, given that it takes more than 8 hours?
Suppose that the time (in hours) required to repair a machine is an exponentially distributed random...

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.8, i.e., mean = 1/lambda. What is (a) the probability that a repair takes less than 77 hours?

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed...

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean =μ39 and standard deviation =σ5. (a) What is the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles? (b) What proportion of tires have lifetimes between 38 and 43 thousand miles? (c) What proportion of tires have lifetimes less than 44 thousand miles? Round the answers to at least four decimal places.