Chapter 7.1, Problem 7.22E

To determine

To find: the simulation to see if the writer’s claim is reasonable.

Explanation of Solution

Given:

250 flip of a coin. Assume that heads and tails are equally likely

There would be 10 possible digits and assigning 5 of the digits to heads and 5 of the digits to tails

Heads: Digit 0, 1, 2, 3, 4

Tails: Digit 5, 6, 7, 8, 9

Using the TI 83 calculator for simulating the result

Generating the 250 flip of a coin using a TI 83/TI84 calculator

  $randInt\left(0,9,250\right)$

Counting the number of heads in every run containing heads

1, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 1, 5, 5, 9, 5, 1, 2, 2, 1, 3, 3, 3, 5, 5, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 5, 5, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 1, 1, 1, 1, 4, 5, 5, 4, 4, 3

After observing that there are 16 ones, 22 twos, 7 threes, 7 four, 12 fives and 1 nine

At least two: 22+7+7+12+1=49

At least three: 7+7+12+1=27

At least four: 7+12+1=20

At least five: 12+1=13

At least six: 1

At least seven: 1

Since all values are close the claimed number of runs, the researcher’s claims appears to be reasonable. (Answer may vary)