Who is the king of late night TV? An Internet survey

Solution :

Step 1 of 5:

Given 52% of the population prefers to watch Jay Leno.

Let 3 late night watchers are randomly selected and asked which of the two talk show hosts they prefer.

Our goal is:

a). We need to find the probability distribution for Y, the number of viewers in the sample

     prefer Leno.

b). We need to to construct a probability histogram for p(y).

c). We need to find the probability that exactly one of the three viewers prefers Leno.

d). We need to to calculate the mean and the Standard deviation.

e). We need to  find the probability that the number of viewers favoring Leno falls within    

      2 Standard deviation of the mean.

a).

Now we have to find the probability distribution for Y, the number of viewers in the sample prefer Leno.

Here  is the person prefer to watch Lenovo TV talk show is .

Here be the event.

Where i=0,1,2,3.

Then the probability of is

P()=52%

P()=0.52

Here  is the person prefer to watch Lenovo TV talk show is .

Here be the event.

Where i=0,1,2,3.

The probability of is

P()= 1-P()

P()= 1-0.52

P()= 0.48

Let Y=0.

Let 3 late night watchers are randomly selected.

Here when all 3 viewers not prefer to watch the Lenovo show.

Then the probability of , is

or

p(0)=p(Y=0)

p(0)=  

p(0)= 0.110592

p(1)=p(Y=1)

p(1)=  

p(1)=

p(1)=

p(2)= p(Y=2)

p(2)=  

p(2)=

p(2)= and

p(3)=p(Y=3)

p(3)=  

p(3)= 0.140608

Therefore, p(0)= , p(1)=, p(2)= and p(3)= 0.140608.