Please provide the solution set. An electronic sensor manufacturer has the following past data regarding the number of sensors that were malfunctioning in different batches produced independently along time.

a) 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) at least 3 will malfunction.

b-2) no more than 5 will malfunction.

b-3) at least 1 but no more than 5 will malfunction.

b-4) What is the expected number of sensors that will malfunction?

Batch index Size of batch i Number of sensors malfunctioning in batch i 1 149 16 125 10 2 3 120 12 4 100 9 5 75 9 6 110 11 7 200 17 8 200 23 9 140 13 10 100 11