5.102 How good is a probability estimate? In Example 8 about Down syndrome, we estimated the probability of a positive test result (predicting that Down syndrome is present) to be P1POS2 = 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?