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:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that:
In each toss, heads or tails are equally as likely, since the coin is fair. So [tex]p = \frac{1}{2} = 0.5[/tex]
Three throws, so [tex]n = 3[/tex]
What is the standard deviation for this distribution?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{3*0.5*0.5} = 0.8660[/tex]
The standard deviation for this distribution is 0.8660.
