Final answer:
The question seeks the binomial probability that exactly 6 out of 12 individuals do not cover their mouths when sneezing, given a probability of 0.0519. To calculate this, one would need the exact individual probability of not covering, which is not provided.
Step-by-step explanation:
The question asks about the probability of a specific outcome using the binomial distribution. In this case, the outcome is that exactly 6 out of 12 individuals do not cover their mouths when sneezing, with the probability of not covering given as 0.0519. However, the provided formula and probability do not appear directly relevant to the student's question because they relate to a different scenario involving 200 trials with a success probability of 0.0128, which pertains to the likelihood of developing a disease.
To correctly answer the student's question, the binomial probability formula would need to be applied with the parameters specific to their scenario (n = 12, p = unknown). Without the exact probability of an individual not covering their mouth when sneezing, we cannot calculate the requested probability. This calculation often requires either a suitable calculator or statistical software capable of computing binomial probabilities.