8 Drinking glasses are sold in packs of 4. The manufacturer conducts a survey to assess the quality of the glasses. The results from a sample of 50 randomly chosen packs are summarised in the following table.
| Number of perfect glasses | 0 | 1 | 2 | 3 | 4 |
| Number of packs | 1 | 3 | 10 | 17 | 19 |
Fit a binomial distribution to the data and carry out a goodness of fit test at the \(10 \%\) significance level.