Question

A coin is tossed 72 times. What is a reasonable prediction for the number of

times the coin will land on tails?

Answer 1

That’s it, the probability of getting tail on a single coin toss times the number of observations.

In this case, 1/2 * 72 = 36

However, there’s something called chance error. How much do you expect the result to differ from the expected value? It can be calculated as follows:

The Standard Deviation of this experiment is √(0.5)(0.5) =0.5

The Standard Error is √72 (0.5) ≈ 4.18330 round to the nearst tenth is 4

So, the expected value is 36, give or take 4.

And since the number of tails in a toss coin experiment is normally distributed, then you can expect the number of tails to be between -2 and +2 SEs from the expected value 95% of the time.

In other words, if you repeat this experiment a large number of times, you can expect to obtain between 27 and 43 tails 95% of the time.

Hope this helps