Define X as the number of underfilled bottles from a filling operation in a carton of 24 bottles. Seventy-five cartons are inspected and the following observations on X are recorded:

Values 0 1 2 3 Frequency 39 23 12 1

(a) Based on these 75 observations, is a binomial distribution an appropriate model? Perform a goodness-of-fit procedure with   0.05.

(b) Calculate the P-value for this test.