Question

If X denotes the number of heads in n tosses of a coin, what is the standard deviation of the fraction of heads, which is X/n? Does this standard deviation get larger or smaller as n gets larger?

Answer 1

Answer:

Step-by-step explanation:

Suppose p is the probability of getting head;

The standard deviation can be computed as:

$S.D = \sqrt{\dfrac{p\times(1-p)}{n}$

Thus, the standard deviation gets smaller as n gets larger

For example;

Let assigned some values to the parameters

Assume the standard deviation is ??

sample proportion p = 0.5

and the sample size n = 20

$S.D = \sqrt{\dfrac{0.5\times(1-0.5)}{20}$

S.D = 0.1118

If the sample size increases to 40

$S.D = \sqrt{\dfrac{0.5\times(1-0.5)}{40}$

S.D = 0.0790

Therefore, we can see that as the standard deviation gets smaller as n gets larger