When members of a philanthropic organization send out a fundraising​ letter, they get a return from about 7​% of the people on their mailing list. They simulated 1000 mailings for samples of size n with success rate p=0.07. The sample statistics from each simulation are shown in the table. Complete parts​a) through​ c). n mean standard dev. 20 0.0692 0.0565 50 0.0692 0.0368 100 0.0703 0.0251 200 0.0705 0.0181 ​a) According to the central limit​ theorem, what should the theoretical mean and standard deviation be for each of the sample​ sizes?   Complete the following table.   n theoretical mean theoretical standard dev.   20 nothing nothing   50 nothing nothing   100 nothing nothing   200 nothing nothing   ​(Round to four decimal places as​ needed.) ​b) How close are the theoretical values to those that were​ observed?     Not close   Very close ​c) At what sample size are you comfortable using the normal approximation based on the​ success/failure condition?     A. 200   B. 20   C. 100   D. 50

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