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 981 of the
2500 televisions are tuned to "Eyewitness News"?
A) Yes
B) No

Question

Quizplus · Accepted Answer

Step 1: Calculate Mean and Standard Deviation

p = 0.36 (proportion of TVs tuned to Eyewitness news)
n = 2500 (sample size)

Mean (μ) = np = 2500 * 0.36 = 900

Standard deviation (σ) = √(np(1-p))
= √(2500 * 0.36 * 0.64)
= 24.5

Step 2: Determine if the outcome is unusual

Unusual values are either less than μ - 2σ or greater than μ + 2σ.

μ - 2σ = 900 - 2 * 24.5 = 851
μ + 2σ = 900 + 2 * 24.5 = 949

Therefore, any result outside the range of 851 to 949 would be considered unusual.

We have 981 TVs tuned to Eyewitness news, which is greater than μ + 2σ. Therefore, it is unusual to find 981 TVs tuned to Eyewitness news out of 2500. So, the answer is A) Yes.

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