Mathematics, 25.07.2019 02:00 machucagm01

According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. suppose you sit on a bench in a mall and observe people's habits as they sneeze. (a) what is the probability that among 18 randomly observed individuals exactly 8 do not cover their mouth when sneezing? (b) what is the probability that among 18 randomly observed individuals fewer than 6 do not cover their mouth when sneezing? (c) would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

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Answer from: nadarius2017

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.

Answer from: iklassibrahim123

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,

$\rm P(X = 8)=\dfrac{18!}{8!\times0!}\times (0.267)^8\times(1-0.267)^(^1^8^-^8^)$

$\rm P(X=8) = 0.0506$

b) The probability that among 18 randomly observed individuals fewer than 6 do not cover their mouth when sneezing is,

$\rm P(X=5)+P(X=4)+P(X=3)+P(X=2)+P(X=1)+P(X=0)=0.6571$

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.

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Answer from: Quest

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3 x =27

8)17.80

Answer from: Quest

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste

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