Question: The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce. Round the answers to 3 significant digits.
a) What is the probability a fill volume is less than 12 fluid ounces? (Round your answer to 4 decimal places.)
b) If all cans less than 12.1 or greater than 12.6 ounces are scrapped, what proportion of cans is scrapped? % (Round your answer to 4 decimal places.)
c) Determine specifications (in ounces) that are symmetric about the mean that include 99% of all cans.
, (Round your answers to 3 decimal places.)
Answer: a) P(x < 12) = ?
z = (12 - 12.4)/0.1 = -4
P(x < 12) = P(z < - 4) = 0.00003 (Ans.) Edit
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