Question

In: Statistics and Probability

A local brewery sells their beer in 330 ml bottles. On average the beer is filled...

A local brewery sells their beer in 330 ml bottles. On average the beer is filled with 328.1 ml with a standard deviation of 0.9 ml. Since it is possible to under-fill the bottle but impossible to fill the bottle with more than 330 ml, the distribution is skewed left. Use this information and Excel functions to answer the following questions, and round your answers to four decimal places.

a. What is the probability that the average fill of a six-pack will be greater than 328.5 ml?   

b. What is the probability that the average fill of a twelve-pack will be greater than 328.5 ml?   

c. What is the probability that the average fill of a twelve-pack will be less than 327.8 ml

Solutions

Expert Solution

The sampling distribution has approximately normal distribution. That is .

a) The probability that the average fill of a six-pack will be greater than 328.5 ml is

The EXCEL function is  

=NORMDIST(5.171145 , 0, 1, TRUE) - NORMDIST(1.0886621 , 0, 1, TRUE)

b) The probability that the average fill of a twelve-pack will be greater than 328.5 ml is

The EXCEL function is  

=NORMDIST(7.3131034 , 0, 1, TRUE) - NORMDIST(1.5396007 , 0, 1, TRUE)

c) The probability that the average fill of a twelve-pack will be less than 327.8 ml

orchestra answered 1 year ago
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