Final answer:
To calculate the probability that exactly 5 out of 18 individuals do not cover their mouths when sneezing, we would use the binomial distribution formula, but the exact probability 'p' of an individual not covering their mouth is required to provide an accurate answer.
Step-by-step explanation:
The probability that among 18 randomly observed individuals, exactly 5 do not cover their mouth when sneezing can be calculated using the binomial distribution. If the probability of one individual not covering their mouth when sneezing is known (let's say 'p'), and if the occurrences are independent, then the probability of exactly 5 out of 18 not covering can be calculated using the formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where 'P(X = k)' is the probability of exactly 'k' successes in 'n' trials, 'C(n, k)' is the combination of 'n' taken 'k' at a time, 'p' is the probability of success on a single trial, and '1-p' is the probability of failure on a single trial.
Unfortunately, without knowing the probability 'p' of an individual not covering their mouth when sneezing, we cannot provide the exact probability. Note that the given probability value of 0.2050 needs the probability 'p' to be accurately calculated.