The television show Greens Anatomy has been successful for m

The television show Green’s Anatomy has been successful for many years. That show recently had a share of 17, meaning that among the TV sets in use, 17% were tuned to Green’s Anatomy. Assume that an advertiser wants to verify that 17% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Green’s Anatomy broadcast.

(Round answers to four decimal places.)

Find the probability that none of the households are tuned to Green’s Anatomy.
P(none) =__________

Find the probability that at least one household is tuned to Green’s Anatomy.
P(at least one) = __________

Find the probability that at most one household is tuned to Green’s Anatomy.
P(at most one) = ___________

If at most one household is tuned to Green’s Anatomy, does it appear that the 17% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Green’s Anatomy unusual?)

__ no, it is not wrong

__ yes, it is wrong

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    11      
p = the probability of a success =    0.17      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.128783142 [ANSWER]

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b)

P(at least one) = 1 - P(0) = 0.871216858 [ANSWER]

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    11      
p = the probability of a success =    0.17      
x = the maximum number of successes =    1      
          
Then the cumulative probability is          
          
P(at most   1   ) =    0.418933112 [ANSWER]

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d)

No, it\'s not wrong, because that event is not rare (happens around 42% of the time).