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The weight of each package of a certain brand of rice is normally distributed, and the average weight and standard deviation are 5 kg and 0.15 kg respectively.
a. If a pack of rice of that brand is randomly selected, What is the probability that it weighs more than 5.2 kg?
b. If 25 packs of rice of this brand are randomly selected as samples,
i. Explain which probability distribution the average weight of the sample will obey
(Outline your reason clearly) and calculate its average and also standard deviation.
ii. What is the probability that the average weight of the sample is less than 5.03 kg?
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