Math Problem Statement
The television show CSI: Shoboygan has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to CSI: Shoboygan. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 13 households have TV sets in use at the time of a CSI: Shoboygan broadcast.
a) Find the probability that none of the households are tuned to CSI: Shoboygan. P(none) = Incorrect
b) Find the probability that at least one household is tuned to CSI: Shoboygan. P(at least one) = Incorrect
c) Find the probability that at most one household is tuned to CSI: Shoboygan. P(at most one) = Incorrect
d) If at most one household is tuned to CSI: Shoboygan, does it appear that the 20% share value is wrong? (Hint: Is the occurrence of at most one household tuned to CSI: Shoboygan unusual?) Use a value of 5% or lower for "unusual".
yes, it is wrong no, it is not wrong
Solution
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Math Problem Analysis
Mathematical Concepts
Binomial Probability
Probability Theory
Formulas
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
P(at least one) = 1 - P(none)
Theorems
Binomial Theorem
Suitable Grade Level
Grades 10-12
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