The Acme Candy Company claims that $60 \%$ of the jawbreakers it produces weigh more than $0.4$ ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be significant for this sample of 800 to contain 494 jawbreakers that weigh more than $0.4$ ounces? Consider as significant any result that differs from the mean by more than 2 standard deviations. That is, significant values are either less than $\mu$ $2 \sigma$ or greater than $\mu + 2 \sigma$.
A) Yes
B) No

Question

Quizplus · Accepted Answer

The expected number of jawbreakers weighing more than 0.4 ounces is $0.6 \times 800 = 480$. The standard deviation is $\sqrt{800 \times 0.6 \times 0.4} = \sqrt{192} \approx 13.86$. The range for non-significant results is $480 \pm 2 \times 13.86$, which is approximately $452.28$ to $507.72$. Since 494 is within this range, it is not significant.

The Acme Candy Company Claims That 60%60 \%60% Of the Jawbreakers It Produces Weigh More Than

The Acme Candy Company Claims That $60 \%$ Of the Jawbreakers It Produces Weigh More Than