Approximate Binomial Probabilities Using the Normal Distribution
-Find the probability that in 200 tosses of a fair six-sided die, a three will be obtained at least 40 times.
A) 0.1210
B) 0.8810
C) 0.0871
D) 0.3875

Question

Quizplus · Accepted Answer

The probability of getting a three on a single toss of a fair six-sided die is 1/6. The mean of the binomial distribution is np = 200 * 1/6 = 33.33, and the standard deviation is sqrt(np(1-p)) = sqrt(200 * 1/6 * 5/6) = 5.77. The probability of getting a three at least 40 times is the same as the probability of getting a three more than 39.5 times, which is the same as the probability of getting a z-score greater than (39.5 - 33.33) / 5.77 = 1.09. Using a standard normal distribution table, we find that the probability of getting a z-score greater than 1.09 is 0.1210.