A quality control inspector accepts shipments of 500 precision ½" steel rods if the mean diameter of a sample of n = 100 falls between 0.4995" and 0.5005". Previous evaluations have established that the standard deviation for individual rod diameters is 0.003".

a. Determine the probability that the inspector will accept an almost out-of-tolerance shipment that actually has H 0.5003 cm.

b. Determine the probability that the inspector will (mistakenly) reject a near-perfect shipment that actually has u = 0.4999 cm.

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.