StatisticsdrillSampling distribution of a proportion
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
10% of all customers of a streaming service renew each year. In a random sample of 100 customers, what is the probability that the sample proportion who renew is below 0.029? Use the normal approximation without a continuity correction. Answers within 0.002 count, so a z table with z rounded to 2 decimals works. Round to 4 decimal places.
What this problem teaches
The approximation is reasonable here because np = 10 and n(1 - p) = 90 are both at least 10.
A hint if you get stuck
The sample proportion is roughly normal with mean p and standard error √(p(1 - p) / n). Use the true p, not the sample value, in the standard error.
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