Beer bottles are filled so that they contain an average of 2

Beer bottles are filled so that they contain an average of 275 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 270 ml of beer? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 270 ml? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

What is the probability that a randomly selected 10-pack of beer will have a mean amount less than 270 ml? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Solution

a) P(bottle having less than 270 ml) = P(X<270) =0.15866