Nylon bars were tested for brittleness. Each of 280 bars was molded under similar situations and was tested by placing a specified stress at 5 locations on the bar. Supposing that each bar has uniform composition, the number of breaks on given bar should be binomially distributed with unknown probability p of breaking. The following table summarizes the outcome of experiment:
Breaks/Bar 0 1 2 3 4 5 total
Frequency 121 110 38 7 3 1 280
Determine using a 99% confidence interval the probability of a bar breaking at the specified stress.