Let X be a discrete binomial random variable.
Let p = 0.267 be the probability that a person does not cover his mouth when sneezing.
Let n = 18 be the number of independent tests.
Let x be the number of successes.
So, the probability that the 18 individuals, 8 do not cover their mouth after sneezing will be:
a) P (X = 8) = 18! / (8! * 10!) * ((0.267) ^ 8) * ((1-0.267) ^ (18-8)).
P (X = 8) = 0.0506.
b) The probability that between 18 individuals observed at random less than 6 does not cover their mouth is:
P (X = 5) + P (X = 4) + P (X = 3) + P (X = 2) + P (X = 1) + P (X = 0) = 0.6571.
c) If it was surprising, according to the previous calculation, the probability that less than 6 people out of 18 do not cover their mouths is 66%. Which means it's less likely that more than half of people will not cover their mouths when they sneeze.
Some parts are missing in the queston. Find attached the picture with the complete question
Answer:

Explanation:
Let's put the information in a table step-by step.
(number of remaining students)
Juniors Seniors
Condition
- Twice juniors as seniors 2(S - 15)
- 3/4 of the juniors left 1/4×2(S - 15)
- 1/3 of seniors left 2/3×(S - 15)
At the end, there were 8 more seniors than juniors:
- 2/3×(S - 15) - 1/4×2(S - 15) = 8
Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.
Solve the equation:



- Addtion property of equalities:


- Division property of equalities:

That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):

Just substitute S with 153 fo find the number of students that remained to perfom in the musical:


An inverse variation can be represented by the equation

We have

Answer: The relationship does not show an inverse variation.
If she went 10 miles upstream in the same time as she went 20 miles downstream, that means the downstream speed is twice the upstream speed.
The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.
9 + c = 2(9 - c)
9 + c = 18 - 2c
3c = 9
c = 3
Answer: The speed of the current is 3 mph.
Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.