Answer:
Check Explanation
Step-by-step explanation:
To set up the probability that fewer than half of 16 cover their mouth while sneezing.
It will be modelled as a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of people observed = 16
x = Number of successes required = less than 8
p = probability of success = probability that one covers his/her nose = 1 - 0.267 = 0.733
q = probability of failure = probability that one doesn't cover his/her nose = 0.267
So, probability of less than 8 people covering their nose is P(X < 8)
And it is given mathematically as a sum of probabilities from 0 person covering his/her nose to 7 people covering their nose
P(X < 8) = Σ ⁿCₓ pˣ qⁿ⁻ˣ (summing from x = 0 to x = 7 with n constant at 16)
P(X < 8) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7)
P(X < 8) = 0.0 + 0.0 + 0.0 + 0.00000772941 + 0.000068964 + 0.0004543875 + 0.00228697031 + 0.00896923079
P(X < 8) = 0.0117872825 = 0.0118 as given in the question.
