To determine the efficiency of a batch of production of electric motors, 8 motors are tested. the average efficiency of the sample is calculated to be 88.5% and the standard deviation of the sample is 0.5 percentage point. (a) determine a 95% confidence interval for the mean efficiency of the (b) if we want to cut the confidence interval to one third, how many more motors should be tested?

Asolid cylinder is concentric with a straight pipe. the cylinder is 0.5 m long and has an outside diameter of 8 cm. the pipe has an inside diameter of 8.5 cm. the annulus between the cylinder ad the pipe contains stationary oil. the oil has a specific gravity of 0.92 and a kinematic viscosity of 5.57 x 10-4 m2/s. most nearly, what is the force needed to move the cylinder along the pipe at a constant velocity of 1 m/s?