(Solved):
Define \( X \) as the number of underfilled bottles from a filling operation ...
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Define \( X \) as the number of underfilled bottles from a filling operation in a carton of 24 bottles. 75 cartons are inspected and the following observations on \( X \) are recorded: (a) Based on these 75 observations, is a binomial distribution an appropriate model? Perform a goodness-of-fit procedure with \( \alpha=0.05 \). (b) Calculate the \( P \)-value for this test.