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A sample of 1300 people is to be used to estimate the proportion of left-handed people. Suppose the true proportion of left-handed people in the population is 12% (which is unknown to the organizers of the observational study).

A) What is the probability that as a result of the survey, the estimate will differ by more than 2% from the true value 12%? Use the normal approximation to solve this problem.

B )What should be the minimal sample size to guarantee that the obtained estimate doesn't differ by more than 2% from the true value 12% with probability at least 99%?