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I received the below statistics question from my teacher please help me to solve it.


When approaching an iceberg, the captain of a ship is trying to estimate its submerged volume in order to determine the safe distance needed to get around the iceberg.

1. The captain asks eleven sailors to make a visual estimate of the emerged volume. From this estimate, he infers the volume of submerged ice knowing that, during solidification of water, the volume of material exactly increases by 10 %. Calculate the reconciled value of the emerged volume, the estimated value of the submerged volume, and the precision of these quantities. The values given by the sailors are:

2000, 1800, 1500, 2000, 2200, 2000, 2500, 2500, 2000, 1000, 2200.

These values are expressed in “titanics”, a fictitious volume unit for icebergs. Beware, one of the sailors drank too much alcohol and his evaluation could be biased.

2. In addition to the visual estimation above, the captain has a measurement of the emerged volume obtained with a radar system. The value provided by the system is
2150 titanics with a standard deviation of 300 titanics. You have to reconcile and estimate volumes and calculate the precision using two methods. The first one consists in using all measurements. The second one is recursive and uses the preceding results and the new measurement. Compare both methods.

3. In addition to previous measurements, the captain has a measurement of the submerged volume given by an acoustic system. The value is 19000 titanics with a standard-deviation of 2000 titanics. Reconcile and estimate volumes and calculate the precision using the previous two methods.

4. Captain doubts that the relationship between emerged and submerged volumes exactly obeys the one used above due to impurities in the water, imperfections of the crystal structure of the iceberg, etc. He decides to take a standard-deviation of 1000 titanics for the residual of the model relating emerged and submerged volumes. According to this, determine new estimations of emerged and submerged volumes and their precision.