By computing the binomial mean and variance and using the empirical rule, one finds that the probability
of obtaining between 40 and 60 heads in 100 tosses of a fair coin is approximately 95%.

Question

Quizplus · Accepted Answer

This statement is true. The binomial mean for n trials with probability of success p is given by np, and the variance is given by np(1-p). For 100 tosses of a fair coin, p=0.5, so the mean is 50 and the variance is 25. Using the empirical rule, we know that approximately 95% of the data falls within 2 standard deviations of the mean. In this case, the standard deviation is the square root of the variance, which is 5. So, we want to find the probability of obtaining between 40 and 60 heads, which is within 2 standard deviations of the mean. Using a normal approximation to the binomial distribution, we can calculate this probability to be approximately 0.9545 or 95%.

By Computing the Binomial Mean and Variance and Using the Empirical