Find the mean, variance, and standard deviation of the binomial distribution. 1) Thirty-six percent of women consider themselves basketball fans. You randomly select six women and ask each if she considers herself a basketball fan.
This is an example of a binomial distribution, where we have a fixed number of trials (n=6) and each trial has only two possible outcomes (success or failure).
The probability of success (p) is given as 0.36, which is the proportion of women who consider themselves basketball fans.
Mean: The mean of a binomial distribution is given by the formula μ = np, where n is the number of trials and p is the probability of success. In this case, the mean is μ = 6 x 0.36 = 2.16.
Variance: The variance of a binomial distribution is given by the formula σ^2 = np(1-p), where n is the number of trials and p is the probability of success. In this case, the variance is σ^2 = 6 x 0.36 x (1-0.36) = 1.38.
Standard deviation: The standard deviation of a binomial distribution is the square root of the variance, so in this case, the standard deviation is σ = sqrt(1.38) = 1.17.