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.

For more information, refer the link given below

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Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

Answer from: Quest

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where, $a = \frac{\sum y \sum x^2 - \sum x\sum xy}{n\sum x^2 - (\sum x)^2}$

here given table is,

price ($), x : 18 23 25 29 30 33

pairs sold, y : 16 13 10 8 6 2

so, $\sum x = 158$ , $\sum y = 55$ , $\sum xy = 1315$ ,

$\sum x^2 = 4308$ and $\sum y^2 = 629$ ,

thus, slop of the given line is,

$a = \frac{55\times 4308-158\times 1315}{6\times 4308-(158)^2}$

⇒ $a = \frac{29170}{884}$

⇒ $a =32.9977375566$ ≈ 33

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According to a study done by a university student, the probability a randomly selected individual wi...