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The number of heads (H) reported by all of you is tabulatedbelow, w here the first column is the number of heads and thesecond column is the number of times it occurred.

0 0

1 0

2 0

3 2

4 6

5 6

6 9

7 3

8 0

9 1

10 0

The number of tails (T) is simply given by H=10-T. The resultsof the coin flip can be expresses mathematically in a simple way byassigning the value 1 the n a heads occurs and 0 when a tailsoccurs. You could choose other numerical assignents, but this oneis convenient because the total numerical value is the number ofheads obtained in each coin flip experiment.

e) The width of the distribution is given byσ=√Npq. What is itfor ourexperiment?

f) Plot the probabilities on the plot you did for part a) usingasuitable over-all normalizing factor to account for the number ofpeople doing the coin flipexperiment.You can find discussions ofthe binomial function in the manual, Yan’s lectures, and on theweb.If your calculator does not do factorials, you can find web-basedones readily. Showyour calculations to get full credit.

(Note - part a -  Plot the results of this experiment,using H on the x-axis and indicating the expected error (√H)) oneach measurement.

g) What fraction of our results for the number of times weobserved a numberof heads agrees with the binomial distribution(after you normalize is to ourexperiment) within our estimatederrors? We will show laterthat about 2/3 ofthem should.