THE CLICK-RATE BAND
Beginner
Difficulty: Easy Tags: Probability & Statistics
Story
A search-ads team reports today's click-through rate to stakeholders every morning, and a bare point estimate without an uncertainty band has burned them before on low-traffic days.
The Math
p_hat = clicks / n
SE = sqrt( p_hat * (1 - p_hat) / n )
interval = p_hat +- z * SE, z = 1.959964 (95% interval)
Input Format
n clicks
Output Format
p_hat lower upper, 6 decimals.
Constraints
1 <= clicks <= n <= 10^9- Time limit: 1.0 second.
Example
Input
1000 45
Output
0.045000 0.032151 0.057849
Keywords
probability-and-statistics
Python
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