Beer bottles are filled so that they contain an average of 335 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 7 ml. [You may find it useful to reference the z table.] a. What is the probability that a randomly selected bottle will have less than 332 ml of beer? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.) b. What is the probability that a randomly selected 6-pack of beer will have a mean amount less than 332 ml? (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Answer:A) 0.3336; B) 0.8531Step-by-step explanation:For part A,We use the z-score formula for an individual score:[tex]z=\frac{X-\mu}{\sigma}[/tex]Our X value is 332, our mean, μ, is 335, and our standard deviation, σ, is 7:z = (332-335)/7 = -3/7 ≈ -0.43Using a z table, we see that the area under the curve less than this (the probability that X is less than this value) is 0.3336.For part B, We use the z-score formula for the mean of a sample:[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]Our X-bar value is 332, our mean, μ, is 335, our standard deviation, σ, is 7, and our sample size, n, is 6:z = (332-335)/(7÷√6) = 3/2.8577 ≈ 1.05Using a z table, we see that the are under the curve to the left of this, or the probability less than this, is 0.8531.