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Question
1. The weight of cereal boxes follows a normal distribution with a mean of 1,000 grams and a standard deviation of 40 grams.
(a) A box is rejected by the quality control department if its weight is below 950 grams. What percentage of boxes will be rejected?
(b) Find the percentage of boxes whose weight is between 980 grams and 1,010 grams.
(c) Find the percentage of boxes whose weight is above 1,010 grams.
(d) Determine the 40th percentile for the weight of the boxes of cereal.
(e) Determine the weight so that only 5% of boxes are heavier than the weight you choose.
(f) Randomly pick five boxes, find the probability that at least one box is rejected.
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