A coin is to be tossed 36 times. a) What are the mean and standard deviation of

Question

A coin is to be tossed 36 times.

a) What are the mean and standard deviation of the number ofheads?
b) Suppose the resulting number of heads is unusual, two standarddeviations above the mean. How many "extra" heads wereobserved?
c) If the coin was tossed 100 times, would you still consider thesame number of extra heads unusual? Explain.
d) In the 100 tosses, how many extra heads would you need toobserve in order to say that the results were unusual?
e) Explain how these results refuse the "Law of Averages" butconfirm the Law of Large Numbers?

Explanation / Answer

p = 0.5 q = 0.5 a) mean = np = 36 * 0.5 = 18    Standard deviation = (npq)                                = (0.5*0.5*18)                                = 2.12 b) Extra heads observed = 2(standard deviation)                                      = (2.12*2)                                      = 4.24 ˜4 c) It will not be same, when the sample size is different, thestandard deviation will change. So, the number of extra heads willdifferent. d) = npq       = (100*0.5*0.5)       = 5 Extra head need to observed = 10 e)Law of large numbers indicate that when the sample size is large,the average of the results obtained will close to the expectedvalue. Law of averages indicate wherever how much the size of thesample. However, when the sample size is small, the result might be easilyto be viewed as unusual due to its small standard deviation. Whenthe sample size is large, results get wont easily fall out of 2standard deviation. This more fulfill the law of large numbers.

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