a) A certain machine produces bulbs and were examined for the number of defectives in a sample of 14. The following table shows the distribution the number of defective items contained in 139 samples:...

Extracted text: a) A certain machine produces bulbs and were examined for the number of defectives in a sample of 14. The following table shows the distribution the number of defective items contained in 139 samples: Number of Defectives in a Sample of 14 Number of Samples 7 1 8 2 20 3 21 4 35 5 30 12 7 1 8 5 i) Fit a binomial distribution and find the expected frequencies if the chance of machine being defective is 0.5 ii) Find the probability of that number of defectives are at least 3. iii) Find the mean and standard deviation of the number of defectives.