Extensive experience with a certain type of fans used in diesel engines has sugg

Question

Extensive experience with a certain type of fans used in diesel engines has suggested that time until failure follows an exponential distribution. Suppose the average time until failure is 25,000 hours.

a)Find the probability that a randomly selected fan will last at most 31,000 hours?

b)If 80 fans of this type were randomly selected, what is the probability that at most 45 of them last for at least 30,000 hours.

If possible, how would i do this using R software. If not then please do it the normal way and ill see if i am gettign the correct answer when using R. Thank you!

Explanation / Answer

Ans:

mean failure time=25000 hr

a)

P(X<=31000)=1-e-(31000/25000)=1-e-1.24=0.7106

Use pexp(31000,rate=1/25000)

b)

P(X>=30000)=e-30000/25000=e-1.2=0.3012

use pexp(30000,rate=1/25000,lower.tail=false)

Now Use Binomial with n=80,p=0.3012

P(y<=45)=BINOMDIST(45,80,0.3012,TRUE)=1

Use pbinom(45, size=80, prob=0.3012)

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