In a recent poll, the Gallup organization found that 45% of adults in America be

Question

In a recent poll, the Gallup organization found that 45% of adults in America believe that the overall stat of moral values in the US is poor. Suppose a survey of a random sample of 20 adults in America is conducted in which they are asked to disclose tbeir feelings on the overall state of moral values in the US

a) Find the probability that exactly 15 of those surveyed feel that the moral is poor.

b) find the probability that no more than 3 of those surveyed feel the state of morals is poor. would it be unusual to have no more than 3 to feel that state of morals is poor? why or why not?

c) find the probability that 10 or 11 believe that the state of morals is poor

d) test for symmetry. if it's symmetric, find the interval of typical values

e) would it be unusual to find 15 or more adults in America who believe the overall state of moral values is poor in the US? Why or Why not? If we found 15 who thought moral values were poor, what would this imply?

Explanation / Answer

Ans:

Binomial distribution with n=20,p=0.45

P(x=r)=20Cr*0.45r*(1-0.45)20-r

a)P(x=15)=20C15*0.4515*0.555=0.0049

b)P(x<=3)=20C0*0.450*0.5520+20C1*0.451*0.5519+20C2*0.452*0.5518+20C3*0.453*0.5517

=0.0000+0.0001+0.0008+0.0040

=0.0049

As,P(x<=3)=0.0049<0.05,so it is unusual event.

c)P(x=10 or 11)=P(x=10)+P(x=11)=20C10*0.4510**0.5510+20C11*0.4511*0.559

=0.1593+0.1185=0.2779

e)P(x>=15)=P(x=15)+P(x=16)+P(x=17)+P(x=18)+P(x=19)+P(x=20)

=0.0049+0.0013+0.0002+0+0+0

=0.0064

As,P(x>=15)=0.0064<0.05,so it is unusual event.

r BINOMDIST(r,20,0.45,FALSE) 0 0.0000 1 0.0001 2 0.0008 3 0.0040 4 0.0139 5 0.0365 6 0.0746 7 0.1221 8 0.1623 9 0.1771 10 0.1593 11 0.1185 12 0.0727 13 0.0366 14 0.0150 15 0.0049 16 0.0013 17 0.0002 18 0.0000 19 0.0000 20 0.0000

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