Question

Using the table for many repetitions of the experiment of tossing a coin 10 times, what is the mean number of heads in 50 repetitions of this experiment and 1,000 repetitions, and which of these sample means is closer to the population mean? Number of Heads 0 1 2 3 4 5 6 7 8 9 10 In 50 Repetitions 0 0 1 5 9 16 10 6 2 1 0 In 200 Repetitions 0 2 8 22 38 55 41 24 9 1 0 In 500 Repetitions 2 5 24 57 111 111 110 56 21 3 0 In 1,000 Repetitions 1 8 43 117 207 248 203 121 45 6 1

Answer 1

When there are 1000 repetitions, the mean will be 5.002.

The charts that you have list the number of total heads when you flip the coin 10 times in each trial.

Multiply the total of each by the number number of heads for that category and divide by 1000.

1 x 0
8 x 1
43 x 2
117 x 3
2017 x 4
248 x 5
203 x 6
121 x 7
45 x 8
6 x 9
1 x 10

If you add up those products and divide by 1000, you have 5.002.

Using the law of large numbers, the experiment with 1000 rolls will be the closest to the theoretical amount.