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:

To test the claim that \(20 \%\) of all cars coming to the workshop need to be repaired, look up the corresponding probabilities in Table 1, calculate the expected frequencies, and perform the chi square test at the 0.05 level of significance.

Data From Table 1

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Number requiring repairs 0 Number of days 25 1 112 234 63 68 12