Poincare's Bread

Detective Story #1: Using distributions
  1. The story goes that every day Poincare bought bread from his local baker. Though the bread was supposed to weigh 1 kilogram, Poicare found that months of careful record keeping produced a nice normal distribution with a mean (average) value of only 950 grams. Poincare called the police and the baker was promptly told to behave himself.

    How did Poincare know?

  2. A year later Poincare again visited the police: Though his own loaves had indeed grown larger, the baker, he declared, was still short-shifting his other customers. The police again confronted the incredulous baker. How, the man asked, could Poincare possibly know that he was always given the largest loaf?

    How did Poincare know?

(Source)

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