The probability of correctly predicting the outcome of a coin toss is p = 1/2.What is the standard deviation of the normal approximation to the binomial distribution for the number of correct predictions in a series of 100 tosses?
A)50
B)25
C)10
D)5

Question

The probability of correctly predicting the outcome of a coin toss is p = 1/2.What is the standard deviation of the normal approximation to the binomial distribution for the number of correct predictions in a series of 100 tosses?​
A)​50
B)​25
C)​10
D)​5

Quizplus · Accepted Answer

The standard deviation of a binomial distribution 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 each trial. For 100 coin tosses with $p = 1/2$, the standard deviation is $\sigma = \sqrt{100 \cdot \frac{1}{2} \cdot \frac{1}{2}} = \sqrt{25} = 5$.

The Probability of Correctly Predicting the Outcome of a Coin