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A firm produces cans of soup. The can weights are normally distributed with a mean of 450 grams and a standard deviation of 15 grams.

A firm produces cans of soup. The can weights are normally distributed with a mean of 450 grams and a standard deviation of 15 grams.

a) If a single can is randomly selected during a production run, find the probability the can weight is less than 430 grams. (4 decimal places)
b) The quality control inspector randomly selects a sample of 38 cans for testing. Find the probability that the sample average weight will be more than 455 grams. (4 decimal places)

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