Beer bottles are filled so that they contain 305 ml of beer

Beer bottles are filled so that they contain 305 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 5 ml. Use Table 1.

What is the probability that a randomly selected bottle will have less than 301 ml of beer? (Round your intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that a randomly selected 9-pack of beer will have a mean amount less than 301 ml? (Round your intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that a randomly selected 14-pack of beer will have a mean amount less than 301 ml? (Round your intermediate calculations to 4 decimal places, \"z\" value to 2 decimal places, and final answer to 5 decimal places.)

Solution

(a) P(X<301) = P((X-mean)/s <(301-305)/5)

=P(Z<-0.8) = 0.2119 (from standard normal table)

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(b)P(xbar<301) = P((xbar-mean)/(s/vn) <(301-305)/(5/sqrt(9)))

=P(Z<-2.4) = 0.0082 (from standard normal table)

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(c)P(xbar<301) = P((xbar-mean)/(s/vn) <(301-305)/(5/sqrt(14)))

=P(Z<-2.99) = 0.00139 (from standard normal table)