Researchers at Carnegie Mellon University developed an algorithm for estimating the sensor motion of a robotic arm by mounting a camera with inertia sensors on the arm. (The International Journal of Robotics Research, Dec. 2004.) Two variables of interest were the error of estimating arm rotation (measured in radians) and the error of estimating arm translation (measured in centimeters). Data for 11 experiments are listed in the table. In each experiment, the perturbation of camera intrinsic and projections were varied.

a. Find and s for translation errors in trials with perturbed intrinsic but no perturbed projections.
b. Find and s for translation errors in trials with perturbed projections but no perturbed intrinsic.
c. A trial resulted in a translation error of 4.5 cm. Is this value an outlier for trials with perturbed intrinsic but no perturbed projections? For trials with perturbed projections but no perturbed intrinsic? What type of camera perturbation most likely occurred for this trial?

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Trial Perturbed Perturbed Rotation Error Translation Intrinsics Projections (radians) Error (cm) 1 No No .0000034 .0000033 2 Yes No .032 1.0 Yes No .030 1.3 4 Yes No .094 3.0 Yes No .046 1.5 6. Yes No .028 1.3 7 No Yes 27 22.9 8 No Yes .19 21.0 No Yes 42 34.4 10 No Yes 57 29.8 11 No Yes 32 17.7