The lifetime of a certain kind of automobile battery follows the exponential distribution with a mean value of 2 years. If the manufacturer wants to limit the percentage of replaced batteries to no more than 15%, find the number of years he should have to guarantee batteries. [The answer should be a number rounded to five decimal places, don't use symbols such as %] Find the probability that a single component operates for at least 3.5 years. [The answer should be a number rounded to five decimal places, don't use symbols such as %]
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The exponential distribution is defined by the parameter \(\lambda\), which is the inverse of the mean. Therefore, we have: \[ \lambda = \frac{1}{\text{mean}} = \frac{1}{2} \] Show more…
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