The document presents two scenarios using the binomial distribution related to individuals not covering their mouths when sneezing. In the first scenario, the probability that exactly 6 out of 12 do not cover their mouths is calculated as 0.0519. The second scenario involves calculating the probability that fewer than 3 individuals do not cover their mouths, with a result to be rounded to four decimal places.

1. (a) Using the binomial distribution, what is the probability that among 12 randomly observed
individuals, exactly 6 do not cover their mouth when sneezing? The probability is 0.0519 . (Round
to four decimal places as needed.) (b) Using the binomial distribution, what is the probability that
among 12 randomly observed individuals, fewer than 3 do not cover their mouth when sneezing?
The probability is (Round to four decimal places as needed.)