Athermocouple outputs a voltage v that depends on temperature t in k) as: v(t) = a +bt+ct2 where a = -12 v, b=0.05 v/k, and c = -1.5 10-5 v/k2. (a) [ic] find the sensitivity of the voltage output as a function of temperature. what is it at nominal body temperature to = 310 k? (b) [ic] a 12-bit analog-to-digital converter (adc) produces a digital output d. find the voltage range that is required of the adc so that the corresponding temperature range spans from 305 k to 315 k (c) estimate the temperature t as a simple linear function of the digital output d of the adc (from 0 to 1023) to be used for a reading display of the temperature sensor. (d) find the worst-case accuracy of this temperature reading over the temperature range. (e) now consider that the voltage of the thermistor is subject to additive white noise with standard deviation of 1 mv. find the precision of the temperature reading obtained from a single sample. how many samples do you need to take for each reading in order for the precision of the sample- averaged output to be better than the accuracy? (hint: think of the central limit theorem.)