The lifetime (X) of a bulb has an exponential distribution with a mean value of (E(X)=8000) hours.

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The lifetime \(X\) of a bulb has an exponential distribution with a mean value of \(E(X)=8000\) hours. Calculate the probabilities

\[P(X \leq 4000), P(X>12000), \quad P(7000 \leq X<9000), \text { and } P(X<4000)\]

(time limits in hours).

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