A student measures the discharge time constant T for a capacitor 4 times, With the following results (in ms): 5.283 4.47, 5.33 and 4.90. (a) Assuming the values follow a normal distribution, What is the best estimate for the true value of the time constant T, and its uncertainty? (4 points) (b) How many total measurements are necessary to reduce the uncertainty calculated in part a) to 0.02 ms? Assume you calculate the same standard deviation for the T distribution even With additional measurements. (3 points) (c) How many measurements out of those calculated in part (b) will be expected to be below 5.4 ms? Use the error integral table (attached). (3 points) Table A. The percentage probability, Prob(within to) = fatto JX - to Gx,o(x) dx, X-to X X+to as a function of t. 0.08 0.09 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0 0.00 0.80 1.60 2.39 3.19 3.99 4.78 5.58 6.38 7.17 0.1 7.97 8.76 9.55 10.34 11.13 11.92 12.71 13.50 14.28 15.07 0.2 15.85 16.63 17.41 18.19 18.97 19.74 20.51 21.28 22.05 22.82 0.3 23.58 24.34 25.10 25.86 26.61 27.37 28.12 28.86 29.61 30.35 0.4 31.08 31.82 32.55 33.28 34.01 34.73 35.45 36.16 36.88 37.59 0.5 38.29 38.99 39.69 40.39 41.08 41.77 42.45 43.13 43.81 44.48 45.15 45.81 46.47 47.13 47.78 48.43 49.07 49.71 50.35 50.98 0.6 51.61 52.23 52.85 53.46 54.07 54.67 55.27 55.87 56.46 57.05 0.7 57.63 58.78 59.35 59.91 60.47 62.11 0.8 58.21 61.02 61.57 62.65 0.9 63.19 63.72 64.24 64.76 65.28 65.79 66.29 66.80 67.29 67.78 71.54 71.99 72.43 1.0 68.27 68.75 69.23 69.70 70.17 70.63 71.09 76.20 76.60 1.1 72.87 73.30 73.73 74.15 74.57 74.99 75.40 75.80 77.37 77.75 78.13 78.50 78.87 79.23 79.59 79.95 80.29 1.2 76.99 80.98 81.32 81.65 81.98 82.30 82.62 82.93 83.24 83.55 1.3 80.64 1.4 83.85 84.15 84.44 84.73 85.01 85.29 85.57 85.84 86.11 86.38 1.5 86.64 86.90 87.15 87.40 87.64 87.89 88.12 88.36 88.59 88.82 1.6 89.04 89.26 89.48 89.69 89.90 90.11 90.31 90.51 90.70 90.90 91.09 91.27 91.46 91.64 91.81 91.99 92.16 92.33 92.49 92.65 1.7 92.81 92.97 93.12 93.28 93.42 93.57 93.71 93.85 93.99 94.12 1.8 1.9 94.26 94.39 94.51 94.64 94.76 94.88 95.00 95.12 95.23 95.34 95.56 95.66 95.76 95.86 95.96 96.06 96.15 96.25 96.34 2.0 95.45 2.1 96.43 96.51 96.60 96.68 96.76 96.84 96.92 97.00 97.07 97.15 2.2 97.22 97.29 97.36 97.43 97.49 97.56 97.62 97.68 97.74 97.80 2.3 97.86 7.91 97.97 98.02 98.07 98.12 98.17 98.22 98.27 98.32 2.4 98.36 98.40 98.45 98.49 98.53 98.57 98.61 98.65 98.69 98.72 98.89 98.92 98.98 99.01 2.5 98.86 99.04 98.76 98.79 98.83 98.95 2.6 99.07 99.09 99.12 99.15 99.17 99.20 99.22 99.24 99.26 99.29 99.33 99 35 99.37 99.39 99 40 99.42 99.44 99.46 99.47 2.7 99.31 99.61 2.8 99.49 99.50 99.52 99.53 99.55 99.56 99.58 99.59 99.60 2.9 99.63 99.64 99.65 99.66 99.67 99.68 99.69 99.70 99.71 99.72 3.0 99.73 3.5 99 95 4.0 99.994 4.5 99.9993 5.0 99.99994
