Answer:
Probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.
Step-by-step explanation:
We are given that a classroom of 20 children in one such area where 13.5% of children are unvaccinated.
If there are no siblings in the classroom, we are willing to consider the vaccination status of the 2020 unrelated children to be independent.
The above situation can be represented through binomial distribution;
where, n = number of trials (samples) taken = 20 children
r = number of success = none of the 20 children
p = probability of success which in our case is probability that
children are unvaccinated, i.e; p = 13.5%
<u><em>Let X = Number of children that are unvaccinated</em></u>
So, X ~ Binom(n = 20, p = 0.135)
Now, Probability that none of the 20 children in such a classroom would be unvaccinated is given by = P(X = 0)
P(X = 0) =
=
= 0.055
<em>Hence, the probability that none of the 20 children in such a classroom would be unvaccinated is 0.055.</em>