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(a) Mr. Sweetheart likes sugar in his hot tea. He buys sugar packets from a local grocery store. Suppose the amount of sugar in a packet follows a normal distribution with mean 2.17 grams and standard deviation 0.08 grams. The amount of sugar in a package should be between 2.13 and 2.21 grams. Otherwise, a packet is considered to be defective.
i. What is the probability that a randomly selected packet is defective?
ii. Three sugar packets are chosen randomly. What is the probability that two of them are not defective?
iii. Mr Sweetheart needs between 8.2 and 9 grams of sugar in a cup of tea for the drink to taste right. One morning, he adds four randomly selected sugar packets. What is the probability that Mr Sweetheart's tea tastes right?
(b) President Fisher posts 2 messages on a social media platform daily on average.
i. What is the probability that he posts no message in three consecutive days?
ii. What is the probability that he posts more than one message in one hour?
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