Question

A local brewery sells their beer in 330 ml bottles. On average the beer is filled with 328.2 ml with a standard deviation of 0.7 ml.

1. Since it is possible to under-fill the bottle but impossible to fill the bottle with more than 330 ml, the distribution is:

Normal

Symmetrical

Skewed Left

Skewed Right

2. Use this information to answer the following questions, and round your answers to four decimal places.
a. What is the z-score for a six-pack with an average fill from all the bottles being 328.7 ml?

b. What is the z-score for a twelve-pack with an average fill from all the bottles being 328.7 ml?

c. What is the z-score for a twelve-pack with an average fill from all the bottles being 328 ml?

You are interested in comparing the local brewery to a large chain. The large chain sells their beer in 330 ml bottles as well. On average the beer is filled with 328.1 ml with a standard deviation of 0.6 ml.

3. Let's consider the large chain.
a. What is the z-score for a six-pack from the large chain with an average fill from all the bottles being 328.7 ml?
b. Are you more likely to see a six-pack from the local brewery or a six-pack from the large chain with an average fill of 328.7 ml?

Local Brewery

Large Chain    

c. Are you more likely to see a twelve-pack from the local brewery or a twelve-pack from the large chain with an average fill of 328 ml?

Local Brewery

Large Chain    

Write smaller number first for both questions below. Round to 2 decimal places.
4. a. At the local brewery the middle 68% of six-packs will have an average fill between  ml and  ml.
b. At the large chain brewery the middle 68% of six-packs will have an average fill between  ml and  ml.

Answer 1