Theory question 112
StatisticsTen coins were tossed together a number of times. The distribution of the number of heads obtained is given in the following table:
Number of Heads: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Frequency: 2, 7, 23, 36, 11, 61, 100, 12, 8, 5, 3
Calculate, correct to three decimal places, the: (a) mean number of heads. (b) probability of getting an even number of heads. (c) probability of getting an odd number of heads.
Show the model answer
Model answer
Σf = 268; Σfx = 0 + 7 + 46 + 108 + 44 + 305 + 600 + 84 + 64 + 45 + 30 = 1333.
(a) Mean = 1333/268 ≈ 4.974.
(b) Even (0, 2, 4, 6, 8, 10): 2 + 23 + 11 + 100 + 8 + 3 = 147; P = 147/268 ≈ 0.549.
(c) Odd: 121/268 ≈ 0.451.
Explanation
Use the relative frequencies from the table.