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

answer set (b) 0.5, 3/4 80% is in order from least to greatest.

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form. typically, the best form in which to evaluate rational numbers is in decimals. in order to convert a percent to a decimal, you would divide the given percentage by 100. you can also accomplish the conversion by moving the decimal point over two places to the left. for example, the decimal value of 80% is 80/100, or 0.8. in order to convert a fraction to a decimal, you need to divide the numerator by the denominator. for example, 3/4 is 0.75. so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.

Answer from: Quest

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

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