QUESTION 3 An engineer studied the failure of pumps used in standby safety syste

Question

QUESTION 3 An engineer studied the failure of pumps used in standby safety systems for commercial nuclear power plants. The number of pumps in this safety system uses six pumps. The engineer found that the probability that a randomly selected pump failed to run after starting was 0.3. Consider a periodic inspection of this system that tests each pump. Expressing probability as a number between 0 and 1, calculate to 3 decimal places (and never specify units or enter text of any kind): The probability that all six pumps fail a periodic inspection is The probability that exactly two pumps fails this inspection is The mean number of pumps that fail is with a variance of and a standard deviation of If over heating can be pevented if at least three pumps operate, the probability of a coolant failure is

Explanation / Answer

Solution - Let be the random variable of the number of pumps that fail after starting,

Then x follows binomial random variable with parameters n = 6 and p = 0.3

then,

P(X=6) = 6c6 * 0.3^6 * 0.7^0

= 0.001

P(X=2)

= 6c2 * 0.3^2 * 0.7^4

= 0.324

Mean of X = n * p

= 6*0.3

= 1.8

and variance = n * p * (1-p)

= 6 * 0.3 * 0.7

= 1.26

so standard deviation = 1.26^0.5

= 1.122

Coolant failure will happen when pumps more than 3 fail out of six so required probability = P( X >3 )

= 0.070

Answers

TY!

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