The Statistical Bulletin published by Metropolitan Life Insurance Co. reported that 2% of all American births result in twins. If a random sample of 8000 births is taken, find the mean, variance, and standard deviation of the number of births that would be result in twins

mean = 160

Variance = 156.8

Standard deviation = 12.52

Step-by-step explanation:

This is solved by the binomial distribution model for approximation.

n = number of random sample in which for this question, n = 8000

p = probability of success = 2% = 0.02

Mean of the sample = Expected value which approximates the average number of cases to expect from the larger sample chosen.

Mean = np = 0.02 * 8000 = 160

Variance = np (1-p) = 160 (1-0.02) = 156.8

Standard deviation = √variance = √156.8 = 12.52