In measuring the power of a three-phase electrical motor running a pump, the following data were obtained (based on one-phase current measurement): v (volts) 460 30.2 0.78 459 31.3 0.80 458
I (amps) 30.4 0.79 460 32.0 0.82 461 31.7
PF 0.81 462 30.7 0.77 0.78 459 31.2 0.80

For a three-phase motor, the power (P) is related to the voltage (V), current (1), and power factor (PF) by the formula P:

P= Vx Ix PF √3

Required:
a. Calculate the mean, the standard deviation, and the random uncertainty of each parameter (V, I, PF, and P) at a 95% confidence level.
b. Calculate the mean value of the power and the random uncertainty of the mean power at a 95% confidence level.
c. If all the measured parameters have an accuracy of 1% of the reading of the measuring device, calculate the systematic uncertainty in the power measurement at a 95% confidence level.
d. Calculate the total uncertainty in the power measurement at a 95% confidence level.