Question

The useful life of a certain valve at a pumping station is normally distributed with a...

The useful life of a certain valve at a pumping station is normally distributed with a mean of 50

months and a standard deviation of five months. Determine the probability that the valve will

wear out after 40 months.

2. Using the information in Question 1, determine the probability that the part will wear out

before its mean life.

3. Using the information in Question 1, determine the probability that the part will wear out

between 45 and 55 months.

Math   Statistics-And-Probability   
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Answer #1

Answer: Let X denote the life of a certain valve at a pumping station. Then,

This implies,

(1) The probability that the valve will wear out after 40 months, is given by

(2) The probability that the valve will wear before its mean life, is given by

(3) The probability that the valve will wear between 45 and 55, is given by

The term is the cdf of standard normal which can be obtained by standard normal table or calculator available online.

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