should have been the minimum number of interviewed citizens? PROBLEM 2 (12 MARKS IN TOTAL). A complex electronic device is made of 10 parts. Over a year, the parts break down independently, with a probability of 0.01. (a) (4 marks) What is the probability of observing at least two breakdowns over a given year? (b) (4 marks) What is the probability of observing three or four breakdowns over a given year? (c) (2 marks) On average, how many breakdowns should be expected over a given year? (d) (2 marks) Calculate the standard deviation of the number of breakdowns over a given year. PROBLEM 3 (12 MARKS IN TOTAL). Squirrel, numerous in the neighborhood, run at full speed on electric cables. A sensor records their flow at a reference point. The following table depicts the record for each of the last 10 observed squirrels i, and the elapsed time t, (in seconds) between two records. Squirrel1 2 3 4 5 6 7 8 9 10 Total 1, (secs) 2 20 15 5 4 8 194 443 3 6 700 (a) (3 marks) Compute the average elapsed time. (b) (5 marks) Compute the standard deviation of the elapsed time. (c) (4 marks) Compute the median of the elapsed time. PROBLEM 4 (19 MARKS IN TOTAL). There are 100 bottles of sparkling water Pschitt in convenience store AllinHere. 40 bottles are from Plant A, and the remaining from Plant B. The level of water in bottles from Plant A is between 0.98 and 1.02 liters versus 0.96 and 1.04 liters for the bottles from Plant B. A customer randomly picks one bottle of Pschitt in the convenience store. The level of water seems to lie between 0.99 and 1 liter. From experiences, it is estimated that 25% of the bottles from Plant A have a level of water between 0.99 and 1 liter, versus 12.5% for those from Plant B. (a) (6 marks) Draw the tree diagram corresponding to the following events: O = < < The level of water in the selected bottle lies in the interval [0.99, 1.00] liter>>; and N = < < The level of water in the selected bottle does not lie in the interval [0.99, 1.00] liter>>. Indicate the corresponding probabilities on each branch of the tree. 2 (b) (6 marks) Calculate the probability of the event O. (c) (6 marks) If event O has been realized, what is the probability that the selected bottle is from Plant A? (d) (1 mark) If the observed level of water in the selected bottle is between 1.02 and 1.04 liters, what is the probability that the bottle is from Plant A?