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Practical Example – Confidence Interval

Practical Example – Confidence Interval

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In the practical example (Al Bundy Shoe Company), the distribution is not a normal distribution but applying central limit theorem (CLT), normal distribution was inferred. When tackling a problem in real life practical situations, does one simply just say they will apply CLT and then infer that the distribution is a normal distribution or does one perform the CLT calculation in order to normalize the distribution before tackling the problem? If it is the latter, how would one go about it using the Al Bundy Shoe Company example?
 
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