Respuesta :
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.
Refer the below solution for better understanding.
Step-by-step explanation:
Given :
The probability that a randomly selected individual will not cover his or her mouth when sneezing is
p = 0.267
Number of independent tests, n = 18
Calculation :
Let x be the number of successes and X be a discrete binomial random variable.
a) The probability that among 18 randomly observed individuals exactly 8 do not cover their mouth when sneezing is,
[tex]\rm P(X = 8)=\dfrac{18!}{8!\times0!}\times (0.267)^8\times(1-0.267)^(^1^8^-^8^)[/tex]
[tex]\rm P(X=8) = 0.0506[/tex]
b) The probability that among 18 randomly observed individuals fewer than 6 do not cover their mouth when sneezing is,
[tex]\rm P(X=5)+P(X=4)+P(X=3)+P(X=2)+P(X=1)+P(X=0)=0.6571[/tex]
c) According to the above 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.
For more information, refer the link given below
https://brainly.com/question/14210034?referrer=searchResults
