easy Probability
A release-checked easy problem for training Exponential/Gamma, Central Limit Theorem.
Tesfa is a scholar, so he is reading a book that's $400$ pages long for fun. The amount of time it takes him to read each page (in minutes) is $\exponential{0.2}$ distributed, independent between pages. Find the approximate time $t$ so that the probability Tesfa finishes reading the book by time $t$ is $97.5\%$. Use the values $\Phi^{-1}(0.95) = 1.65$ and $\Phi^{-1}(0.975) = 1.96$.
This Probability problem is tagged Exponential/Gamma, Central Limit Theorem. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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