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A machine has 6 heat conductors, each with a life time that follows a lognormal distribution...

A machine has 6 heat conductors, each with a life time that follows a lognormal distribution with mean 866 hours and standard deviation 40 hours. The machine needs to have at least 4 working conductors to run.

a. What is the chance that the machine will run for at least 900 hours if the 6 conductors were just replaced?

b. If there are 400 heat conductors, what is the probability that no more than 90 will run for at least 900 hours?

Math   Statistics-And-Probability   
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Answer #1

Answer:-

Given That:-

A machine has 6 heat conductors, each with a life time that follows a lognormal distribution with mean 866 hours and standard deviation 40 hours. The machine needs to have at least 4 working conductors to run.

Lognormal distribution

(1)probability density

Mean = 866 Hours and SD = 40 Hours

a. What is the chance that the machine will run for at least 900 hours if the 6 conductors were just replaced?

The chance that the machine will run for at least 900 hours if the 6 conductors were just replaced

P(atlest 900 hours)

b. If there are 400 heat conductors, what is the probability that no more than 90 will run for at least 900 hours?

p=0.6545,n=400 and x=<90

Therefore P(No more than 90 will be run for atlest 900 hours)=<0.001

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