# Question: In Example 8 about Down syndrome we estimated the probability

In Example 8 about Down syndrome, we estimated the probability of a positive test result (predicting that Down syndrome is present) to be P(POS) = 0.257, based on observing 1355 positive results in 5282 observations. How good is such an estimate? From Section 4.2, 1/1n is an approximate margin of error in estimating a proportion with n observations.

a. Find the approximate margin of error to describe how well this proportion estimates the true probability, P(POS).

b. The long run in the definition of probability refers to letting n get very large. What happens to this margin of error formula as n keeps growing, eventually toward infinity? What’s the implication of this?

a. Find the approximate margin of error to describe how well this proportion estimates the true probability, P(POS).

b. The long run in the definition of probability refers to letting n get very large. What happens to this margin of error formula as n keeps growing, eventually toward infinity? What’s the implication of this?

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