An electronic sensor manufacturer has the following past data regarding the number of sensors that were malfunctioning in different batches produced independently along time. Batch Size of Number of sensors index batch i malfunctioning in batch i 1 149 16 2 125 10 3 120 12 4 100 9 5 75 9 6 110 11 7 200 17 8 200 23 9 140 13 10 100 11 a) (5 points) Find an estimate for the probability of an electronic sensor malfunctioning by considering all the past data available. b) A random sample of 12 sensors is chosen. Find the probability that: b-1) (7 points) at least 3 will malfunction. b-2) (7 points) no more than 5 will malfunction. b-3) (7 points) at least 1 but no more than 5 will malfunction. b-4) (4 points) What is the expected number of sensors that will malfunction? b-5) (5 points) What is the standard deviation of the number of sensors that will malfunction? Hint: Model the number of malfunctioning sensors out of 12 as Binomial r.v