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. 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 328.6 ml?

B) What is the z-score for a twelve-pack with an average fill from all the bottles being 328.6 ml?

C) What is the z-score for a twelve-pack with an average fill from all the bottles being 327.9 ml?

Answer 1

Part A.

n = 6

x =328.6

Z score formula :

Z = 1.3997            ( rounded to 4 decimal place )

Answer : the z-score for a six-pack with an average fill from all the bottles being 328.6 ml is 1.3997  

Part B

n = 12 , x bar = 328.6

Z = 1.9795

Answer : the z-score for a twelve-pack with an average fill from all the bottles being 328.6 ml is 1.9795

Part C

n = 12 , X bar = 327.9

Z = -1.4846

Answer : the z-score for a twelve-pack with an average fill from all the bottles being 327.9 ml is -1.4846