The number of comments per post on a social media site is exponentially distributed, with the average post receiving ten comments. What percentage of posts get fewer than three comments? More than 50? Between five and ten?
What will be an ideal response?
We find ? = 1 / 10 = .1, so that pr(X < x) = 1 - e^(-?x) = 1 - e^(-.1x)
Thus, the percentage of posts that get fewer than 3: pr(X < 3) = 1 - e^(-.1 * 3) = .259
More than 50: pr(X > 50) = 1 - pr(X < 50) = e^(-.1 * 50) = .007
Between 5 and 10: pr(X > 5) - pr(X > 10) = e^(-.1 * 5) - e^(-.1 * 10) = .607 - .368 = .239
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