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The time between failures for an appliances is exponentially distributed with a mean of 25 months....

The time between failures for an appliances is exponentially distributed with a mean of 25 months. What is the probability that the next failure will not occur before 32 months have elapsed? Report answer to 4 decimal places

Math   Statistics-And-Probability   
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Answer #1

Let X = amount of time (in months) between failures for an appliances . The time is known to have an exponential distribution with mean = 25 months.

X ~ Exp(1/25)

The probability density function of X is given by:

The probability that the next failure will not occur before 32 months have elapsed i.e. P(X>32)

                             

                            

                            

                            

Answer: 0.2780

                           

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