Question

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). What is the standard deviation for this distribution?

Answer 1

Answer:

The standard deviation for this distribution is 0.8660.

Step-by-step explanation:

For each coin toss, there are only two possible outcomes. Either it is heads, or it is tails. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that:

In each toss, heads or tails are equally as likely, since the coin is fair. So $p = \frac{1}{2} = 0.5$

Three throws, so $n = 3$

What is the standard deviation for this distribution?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{3*0.5*0.5} = 0.8660$

The standard deviation for this distribution is 0.8660.