The distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is d=|d1−d2| / (√a2+b2+c2). find equations of the planes that are parallel to the plane x + 2y − 2z = −1 and three units away from it. (enter your answers as a comma-separated list of equations.)

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.