With reference to Exercise 10.42, verify that the mean of the observed distribution is 1.6 , corresponding to \(40 \%\) of the cars requiring repairs. Then look up the probabilities for \(n=5\) and \(p=0.25\) in Table 1, calculate the expected frequencies, and test at the 0.05 level of significance whether the binomial distribution with \(n=5\) and \(p=0.25\) provides a suitable model for the situation.

Data From Exercise 10.42

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10.42 An engineer takes samples on a daily basis of n = 5 cars coming to a workshop to be checked for repairs and on 250 consecutive days the data summarized in the following table are obtained: Number requiring repairs 0 Number of days 25 112 1234 63 68 12