Question
Determine the probability P ( 10 or more ) for a binomial experiment with n=11 trials and success probability p=0.6. Then find the mean, variance and standard deviation
Answers
GPT 3.5
To determine the probability P(10 or more) for a binomial experiment with n=11 trials and success probability p=0.6, we need to calculate the individual probabilities of getting exactly 10 successes and exactly 11 successes, and then sum them up.
P(10) = (11 choose 10) * (0.6)^10 * (0.4)^1 = 11 * 0.6^10 * 0.4 = 0.382785 => P(11) = (11 choose 11) * (0.6)^11 * (0.4)^0 = 1 * 0.6^11 * 1 = 0.233474
P(10 or more) = P(10) + P(11) = 0.382785 + 0.233474 = 0.616259
Next, we can calculate the mean, variance, and standard deviation of the binomial distribution.
Mean (μ) = np = 11 * 0.6 = 6.6
Variance (σ^2) = np(1-p) = 11 * 0.6 * 0.4 = 2.64
Standard Deviation (σ) = √σ^2 = √2.64 = 1.62
Therefore, the probability P(10 or more) is 0.616259, the mean is 6.6, the variance is 2.64, and the standard deviation is 1.62.
P(10) = (11 choose 10) * (0.6)^10 * (0.4)^1 = 11 * 0.6^10 * 0.4 = 0.382785 => P(11) = (11 choose 11) * (0.6)^11 * (0.4)^0 = 1 * 0.6^11 * 1 = 0.233474
P(10 or more) = P(10) + P(11) = 0.382785 + 0.233474 = 0.616259
Next, we can calculate the mean, variance, and standard deviation of the binomial distribution.
Mean (μ) = np = 11 * 0.6 = 6.6
Variance (σ^2) = np(1-p) = 11 * 0.6 * 0.4 = 2.64
Standard Deviation (σ) = √σ^2 = √2.64 = 1.62
Therefore, the probability P(10 or more) is 0.616259, the mean is 6.6, the variance is 2.64, and the standard deviation is 1.62.