According to a study done by a university student, the probability a randomly se

Question

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 10 randomly observed individuals exactly 5 do not cover their mouth when sneezing? (b) What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing? (c) Would you be surprised if, after observing 10 individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly 5 individuals do not cover their mouth is Round to four decimal places as needed.) (b) The probabilty that fewer than 3 individuals do not cover their mouth is (Round to four decimal places as needed.) be surprising because the probability of observing fewer than half covering their mouth when sneezing is which T an unusual even (c) This Round es as needed. would is not would not is

Explanation / Answer

Ans:

Binomial distribution with n=10,p=0.267

P(x=k)=10Ck*0.267k*(1-0.267)10-k

a)P(x=5)=10C5*0.2675*(1-0.267)5=0.0724

b)P(x<3)=P(x=0)+P(x=1)+P(x=2)=0.0448+0.1631+0.2673=0.4752

c)P(fewer than half cover their mouth)=

P(more than half do not Cover)=P(P(x>5)=P(x=6)+P(x=7)+P(x=8)+P(x=8)+P(x=10)

=0.0220+0.0046+0.0006+0.0001+0.0000=0.0272

(consider 0.0273 too,as rounding off error may appear)

This would be surprising, as,above probbaility is <0.05,this is an unusual event.

x p(x) 0 0.0448 1 0.1631 2 0.2673 3 0.2597 4 0.1655 5 0.0724 6 0.0220 7 0.0046 8 0.0006 9 0.0001 10 0.0000

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