easy Probability
A release-checked easy problem for training Central Limit Theorem.
$100$ students are walking on the roof of a house. The weight of each student is random with mean $70$ kg and standard deviation $15$ kg, independently between students. Approximate the probability that the mean weight of the students exceeds $73$ kg. The answer will be in the form $\Phi(a)$ for some real $a$. Find $a$.
This Probability problem is tagged 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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