Find the standard deviation of the binomial random variable.
-A die is rolled 17 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.
A)1.543
B)2.06
C)1.537
D)1.491

Question

Find the standard deviation of the binomial random variable.
-A die is rolled 17 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos. 
A)1.543
B)2.06
C)1.537
D)1.491

Quizplus · Accepted Answer

The standard deviation of a binomial random variable is given by the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials, and $p$ is the probability of success on a single trial. For a die roll, the probability of getting a two (success) is $1/6$, and the number of trials is 17. Thus, $\sigma = \sqrt{17 \cdot (1/6) \cdot (5/6)} \approx 1.537$.

Find the Standard Deviation of the Binomial Random Variable