Answer: kindly check explanation
Step-by-step explanation:
Probability of not covering mouth = p(success) = 0.267
Hence, p(covering mouth) = 1 - 0.267 = 0.733
a) What is the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing?
Number of samples (n) = 12
P(X = 8)
Using binomial distribution :
P(x) = nCx * p^x * (1-p)^(n-x)
P(x =8) = 12C8 * 0.267^8 * 0.733^(12-8)
P(x =8) = 12C8 * 0.267^8 * 0.733^4
= 0.00369
b) What is the probability that among 12 randomly observed individuals fewer than 6 do not cover their mouth when sneezing?
P(X < 6) = p(5) + p(4) + p(3) + p(2) + p(1) + p(0)
To save computation time, we can use an online binomial probability calculator :
P(X < 6) = 0.9275
C.) Yes, I will be surprised, because from the binomial probability obtained above, there is a high probability (0.9275) that fewer than half do not cover their mouth.
