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 $\mu + 2 \sigma$.
-A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 541 consumers who recognize the Dull Computer Company name?
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if the outcome is unusual, we calculate the expected mean and standard deviation for the survey results. The mean ($\mu$) is given by $n \times p = 800 \times 0.68 = 544$, where $n = 800$ is the number of trials and $p = 0.68$ is the probability of success (recognizing the company). The standard deviation ($\sigma$) is given by $\sqrt{n \times p \times (1-p)} = \sqrt{800 \times 0.68 \times (1-0.68)} \approx 13.86$. The range for usual outcomes is $\mu \pm 2\sigma = 544 \pm 2 \times 13.86$, which is approximately $544 \pm 27.72$. Since 541 falls within this range, it is not 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