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A snack-food company produces potato chips on three different production lines. Line 1 produces 20% of the total output, Line 2 produces 30% and Line 3 produces the rest. Each line is sampled to ensure the salt content is within the proper range. Historically, 4% of Line 1's output does not meet salt standards, 3% of Line 2's fails to meet the standards, and 2% of Line 3's does not meet the salt standards.
a) Construct a tree diagram to represent this problem.
b) What proportion of potato chip production does not meet the salt standard?
c) What proportion of potato chip production is on Line 1 and meets the salt standard?
d) A randomly selected bag of potato chips is selected and found to meet the salt standard. What is the probability is was made on Line 1?
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