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 12 randomly observed individuals exactly 4 do not cover their mouth when​ sneezing? ​(​b) What is the probability that among

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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
12
randomly observed individuals exactly
4
do not cover their mouth when​ sneezing?
​(​b)
What is the probability that among
12
randomly observed individuals fewer than
6
do not cover their mouth when​ sneezing?
​(​c)
Would you be surprised​ if, after observing
12
​individuals, fewer than half covered their mouth when​ sneezing? Why?
​(​a)
The probability that exactly
4
individuals do not cover their mouth is
nothing.
​(Round to four decimal places as​ needed.)
​(​b)
The probability that fewer than
6
individuals do not cover their mouth is
nothing.
​(Round to four decimal places as​ needed.)
​(​c)
Fewer than half of
12
individuals covering their mouth
 
 
be surprising because the probability of observing fewer than half covering their mouth when sneezing is
nothing​,
which
 
is not
is
an unusual event.
​(Round to four decimal places as​ needed.)
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