A drink manufacturer produces iced tea in bottles advertised as containing 600 mL. TI machines producing these drinks are set so that the average volume dispensed into each bottle 601 mL with standard deviation 1.84 mL. The volumes dispensed into each bottle are distribut normally. a Find the probability that an individual randomly selected bottle contains less than 598 m b Find the probability that a randomly selected pack of 12 bottles has average volume le than 600 mL. c To ensure companies meet their advertising claims, the government specifies that a random

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9 A drink manufacturer produces iced tea in bottles advertised as containing 600 mL. The
machines producing these drinks are set so that the average volume dispensed into each bottle is
601 mL with standard deviation 1.84 mL. The volumes dispensed into each bottle are distributed
normally.
a Find the probability that an individual randomly selected bottle contains less than 598 mL.
b Find the probability that a randomly selected pack of 12 bottles has average volume less
than 600 mL.
c To ensure companies meet their advertising claims, the government specifies that a randomly
selected pack of 12 bottles must have average contents no less than the advertised amount.
The company wants less than 1% chance of failing to meet the requirement.
Find, to the nearest 0.1 mL, what the average volume dispensed by the machine needs to
be, assuming the standard deviation is unchanged.
Transcribed Image Text:9 A drink manufacturer produces iced tea in bottles advertised as containing 600 mL. The machines producing these drinks are set so that the average volume dispensed into each bottle is 601 mL with standard deviation 1.84 mL. The volumes dispensed into each bottle are distributed normally. a Find the probability that an individual randomly selected bottle contains less than 598 mL. b Find the probability that a randomly selected pack of 12 bottles has average volume less than 600 mL. c To ensure companies meet their advertising claims, the government specifies that a randomly selected pack of 12 bottles must have average contents no less than the advertised amount. The company wants less than 1% chance of failing to meet the requirement. Find, to the nearest 0.1 mL, what the average volume dispensed by the machine needs to be, assuming the standard deviation is unchanged.
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