An engineer measures a sample of 5000 dowel pins out of a certain shipment. He finds that the dowel pins have an average diameter of 3.55 mm and a standard deviation of 0.3 mm. Assume the pin diameter follows a Gaussian distribution.

a) What percentage of the shipment of dowel pins will have a diameter between 3.13 mm and 3.95 mm?

b) How many of these dowel pins fall under 25% of the population?

c) What percentage of the shipment of dowel pins will have a diameter between 3.40 mm and 3.75 mm?

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