Suppose we are seeing how well a piece of computer software

Suppose we are seeing how well a piece of computer software can predict people\'s choices for orange juice. Let X =1 if the predictor is wrong and Xi =0 if the predictor is correct. The sample mean (Xn= sum of Xi with i=1 to n) is the observed error rate. Assume each Xi as Bernoulli with unknown parameter p. We would like to understand how our sample mean estimates this unknown quantity (note that our goal is different from the goal of descriptive statistics!). For this entire exercise, use Chebyshev\'s inequality. How many observations n are needed so that the sample mean is 95% likely to be within 0.1 of p? What is the probability that the sample mean is within 0.1 of p given 50 observations?

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