Question

A fair coin is tossed 16 times.
What is the standard deviation for the number of heads?

Answer 1

Two ,four ,six and eight

Answer 2

The standard deviation for the number of heads is 4.

Step-by-step explanation:

The formula for standard deviation is $\sqrt{npq}$

where n is the number of trials, p is the probability of a success for any trial and q is the probability of a failure for any trial.

Since, a fair coin is tossed 16 times, we have $n=16$

In fair coin, the probability of getting heads is $p=0.5$ and the probability of getting tails is

$q=1-p$

$=1-0.5$

$=0.5$

The standard deviation for the number of heads is given by

$\sqrt{npq}=(16)(0.5)(0.5)$

$=4$

Hence, when a fair coin is tossed 16 times, the standard deviation for the number of heads is 4.