Complete Question
The complete question is shown on the first uploaded image
Answer:
a
b

c

I would be surprised because the value is very small , less the 0.05
Step-by-step explanation:
From the question we are told that
The probability a randomly selected individual will not cover his or her mouth when sneezing is 
Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent
Hence for a randomly selected variable X we have that

The probability distribution function for binomial distribution is

Considering question a
Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as

Here C denotes combination
So

Considering question b
Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
![P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)]](https://tex.z-dn.net/?f=P%28X%20%3C%20%205%20%29%20%3D%5BP%28X%20%3D%200%20%29%20%2B%20%5Ccdots%20%2B%20P%28X%20%3D%204%29%5D)
=>
=> 
=> 
Considering question c
Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as

=> ![P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)]](https://tex.z-dn.net/?f=P%28X%20%3E%206%29%20%3D%201%20-%20%5BP%28X%20%3D%200%29%20%2B%20%5Ccdots%20%2B%20P%28X%20%3D6%29%5D)
=> ![P(X > 6)=1 - [^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 * (0.267)^6 * (1- 0.267)^{12-6} ]](https://tex.z-dn.net/?f=%20P%28X%20%3E%206%29%3D1%20-%20%5B%5E%7B12%7D%20C_0%20%2A%20%20%280.267%29%5E0%20%2A%20%20%281-%200.267%29%5E%7B12-0%7D%2B%20%5Ccdots%20%2B%20%5E%7B12%7D%20C_4%20%2A%20%20%280.267%29%5E6%20%2A%20%20%281-%200.267%29%5E%7B12-6%7D%20%5D)
=>
=> 
I would be surprised because the value is very small , less the 0.05