1. Use a table of random numbers to simulate a series of 200 coin tosses. Record
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Question
1. Use a table of random numbers to simulate a series of 200 coin tosses. Record even digits (0,2,4,6,8) as heads and odd numbers (1, 3, 5, 7, 9) as tails. Record your results in an Excel spreadsheet with 0 for heads and 1 for tails.
a. Calculate the cumulative frequency at each toss for throwing a tail.
b. Record the relative frequency of throwing a tail and throwing a head for the entire experiment.
c. Explain whether or not your experimental values match the theoretical distribution.
d. Do your results appear to be random (Justify your answer).
2. Repeat the experiment above using a real coin.
a. Calculate the cumulative frequency at each toss for throwing a tail.
b. Record the relative frequency of throwing a tail and throwing a tail for the entire experiment.
c. Explain whether or not your experimental values match the theoretical distribution.
d. How do the results of your two experiments compare?
3. Collect data (just the final tally of heads/tails for both experiments) from the rest of your group and
a. Record the relative frequency of throwing a tail and throwing a tail for the entire experiment.
b. How do the results of your individual experiments compare with those of the group?
c. Explain whether or not your group's experimental values match the theoretical distribution.
d. Does the Law of Large Numbers seem to be working as advertised?
Explanation / Answer
(1)
(b) Relative frequency for H = 87/200, relative frequency for T = 113/200
(c) As per the theoretical distribution, number of H = number of T = 100. The sample distribution does not match the theoretical distribution
(d) They are not random. Over many many flips, number of H = number of T.
(a) Coin tosses Random # Result Cumulative Tails 4 H 0 5 T 1 7 T 2 5 T 3 0 H 3 8 H 3 3 T 4 3 T 5 5 T 6 1 T 7 2 H 7 1 T 8 0 H 8 9 T 9 6 H 9 7 T 10 7 T 11 6 H 11 4 H 11 5 T 12 2 H 12 5 T 13 5 T 14 5 T 15 9 T 16 2 H 16 3 T 17 2 H 17 1 T 18 0 H 18 0 H 18 5 T 19 0 H 19 1 T 20 7 T 21 3 T 22 3 T 23 3 T 24 5 T 25 3 T 26 9 T 27 1 T 28 3 T 29 3 T 30 2 H 30 9 T 31 7 T 32 5 T 33 7 T 34 1 T 35 9 T 36 7 T 37 6 H 37 3 T 38 1 T 39 9 T 40 6 H 40 3 T 41 9 T 42 7 T 43 0 H 43 3 T 44 4 H 44 9 T 45 2 H 45 3 T 46 4 H 46 4 H 46 2 H 46 4 H 46 8 H 46 1 T 47 7 T 48 6 H 48 6 H 48 5 T 49 5 T 50 8 H 50 5 T 51 7 T 52 1 T 53 3 T 54 1 T 55 1 T 56 6 H 56 0 H 56 8 H 56 8 H 56 0 H 56 1 T 57 3 T 58 9 T 59 0 H 59 7 T 60 5 T 61 2 H 61 5 T 62 5 T 63 4 H 63 8 H 63 4 H 63 4 H 63 9 T 64 0 H 64 8 H 64 7 T 65 1 T 66 0 H 66 3 T 67 5 T 68 3 T 69 1 T 70 0 H 70 2 H 70 2 H 70 1 T 71 3 T 72 3 T 73 3 T 74 2 H 74 7 T 75 2 H 75 4 H 75 9 T 76 0 H 76 1 T 77 6 H 77 5 T 78 5 T 79 0 H 79 4 H 79 2 H 79 0 H 79 6 H 79 5 T 80 4 H 80 6 H 80 5 T 81 0 H 81 1 T 82 8 H 82 0 H 82 1 T 83 8 H 83 0 H 83 9 T 84 9 T 85 2 H 85 7 T 86 5 T 87 7 T 88 6 H 88 7 T 89 6 H 89 5 T 90 5 T 91 8 H 91 3 T 92 1 T 93 3 T 94 7 T 95 8 H 95 7 T 96 4 H 96 0 H 96 0 H 96 9 T 97 9 T 98 3 T 99 3 T 100 4 H 100 6 H 100 3 T 101 5 T 102 8 H 102 7 T 103 4 H 103 4 H 103 6 H 103 6 H 103 1 T 104 4 H 104 6 H 104 6 H 104 1 T 105 9 T 106 7 T 107 3 T 108 5 T 109 4 H 109 4 H 109 6 H 109 8 H 109 3 T 110 5 T 111 4 H 111 8 H 111 6 H 111 9 T 112 7 T 113Related Questions
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