The television show Green’s Anatomy has been successful for many years. That sho
ID: 3380255 • Letter: T
Question
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
Explanation / Answer
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]
*****************
b)
P(at least one) = 1 - P(0) = 0.871216858 [ANSWER]
*****************
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]
*******************
d)
No, it's not wrong, because that event is not rare (happens around 42% of the time).
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