Solving a Statistics Problem: Estimating Unpopped Popcorn Kernels

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The discussion revolves around estimating the proportion of unpopped popcorn kernels based on an experiment where 773 kernels were popped, resulting in 86 unpopped kernels. Participants are tasked with constructing a 90 percent confidence interval for the unpopped kernel proportion and checking the normality assumption. The conversation also explores the effectiveness of the Very Quick Rule for this scenario and questions the typicality of the sample used. The inquiry about whether this is a homework assignment suggests an educational context for the problem-solving approach. Overall, the thread focuses on statistical methods applied to a practical popcorn popping scenario.
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Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, the unpopped kernels were counted. There were 86.

How do I do this?

(a) Construct a 90 percent confidence interval for the proportion
of all kernels that would not pop. (b) Check the normality assumption. (c) Try the Very Quick
Rule. Does it work well here? Why, or why not? (d) Why might this sample not be typical?
 
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What is the Very Quick Rule?

Is this homework?
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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