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