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 $\mu + 2 \sigma$.
-The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 463 jawbreakers that weigh more than .4 ounces?
A)Yes
B)No

Question

Quizplus · Accepted Answer

To determine if the outcome is unusual, we calculate the mean and standard deviation for the distribution of the sample proportion. The mean of the sample proportion ($\mu_{\hat{p}}$) is equal to the population proportion, which is 0.60. The standard deviation of the sample proportion ($\sigma_{\hat{p}}$) is calculated using the formula $\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$, where $p = 0.60$ and $n = 800$. Thus, $\sigma_{\hat{p}} = \sqrt{\frac{(0.60)(0.40)}{800}} = \sqrt{\frac{0.24}{800}} = \sqrt{0.0003} = 0.0173$.To find if 463 out of 800 is unusual, we convert 463 to a proportion: $\frac{463}{800} = 0.57875$. We then compare this to the mean ($0.60$) in terms of standard deviations. The difference from the mean is $0.60 - 0.57875 = 0.02125$, which is less than 2 standard deviations ($2 \times 0.0173 = 0.0346$).Since the difference from the mean is less than 2 standard deviations, the result 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