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StatisticsQ&A LibraryThe time to failure of a certain type fo electrical component is assumed to follow an exponential distribution with a mean of 4 years. The manufacturer replaces free all components that fail while under guarantee.If the manufacturer wants to replace a maximum of 3% of the ocmponents, for how long should the manufacturer's stated guarantee on the component be?Question

Asked Feb 11, 2020

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The time to failure of a certain type fo electrical component is assumed to follow an exponential distribution with a mean of 4 years. The manufacturer replaces free all components that fail while under guarantee.

If the manufacturer wants to replace a maximum of 3% of the ocmponents, for how long should the manufacturer's stated guarantee on the component be?

Step 1

Consider *X *be a random variable which follows exponential distribution indicates the failure time of a component. The mean is provided as 4 years.

The expression for the cumulative distribution function is given by:

So, the mean of random variable, *X* is,

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