Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$.
-According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be unusual to find that 986 of the 2500 televisions are tuned to "Eyewitness News"?
A)Yes
B)No

Question

Quizplus · Accepted Answer

Given that 36% of televisions are tuned to "Eyewitness News," the expected number of televisions tuned in out of 2500 is $2500 \times 0.36 = 900$. The standard deviation ($\sigma$) for a binomial distribution is calculated using the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials and $p$ is the probability of success. Substituting the given values, $\sigma = \sqrt{2500 \cdot 0.36 \cdot (1-0.36)} = \sqrt{2500 \cdot 0.36 \cdot 0.64} \approx 24$. The range for usual outcomes is $\mu - 2\sigma$ to $\mu + 2\sigma$, or $900 - 2 \cdot 24$ to $900 + 2 \cdot 24$, which simplifies to $852$ to $948$. Since 986 is outside this range, it is considered unusual.

Determine If the Outcome Is Unusual μ−2σ\mu - 2 \sigmaμ−2σ Or Greater Than

Determine If the Outcome Is Unusual $\mu - 2 \sigma$ Or Greater Than