Assume that n = 15, and p = 6 7 . Find the probability of at least 2 successes and at least 1

Question

involving the computation of probabilities for a Bernoulli trial.

Answer 1

mean = np = 15(6/7) = 90/7 = about 12.8571

standard deviation = sqr(npq) = sqr((90/7)(1/7) = (3/7)sqr10 = about 1.3553

Probability of at least 2 successes is (12.8571-2)/SD = 10.8571/1.3553 = about 8 standard deviations from the mean. with the empirical rule 3 standard deviations from the mean include 99.7% of the results, leaving .99.7+.15 =at least 99.85% probability of at least 3 standard deviations of the mean. With 8, the probability goes higher, probabbly above 99.99%

Probability of at least one success and the odds go higher, maybe 99.999%+