We use the measurements of voltage (U) and resistance (R) to calculate the power (P) of a joule heater via the equation of P=U/R. (a) U is measured for four times at the same condition to be 3.62, 3.61, 3.56, and 3.50 V. Calculate the mean value ( U) and the uncertainty (AU) at the confidence level of 99%. (b) Derive AP as a function of U. R. AR. and AU. (c) If R = 2.52 Q and the true standard deviation of R is stable at 0.10 Q. How many times do we need to repeat the measurement of R to reduce AP to below 0.25 W at the confidence level of 99%.