A Manufacturer of NFL Regulation Footballs Uses a Machine to Inflate

A manufacturer of NFL regulation footballs uses a machine to inflate its new balls to a pressure of 13.5 pounds (σ = .1) . When the machine is properly calibrated, the mean inflation pressure is 13.5 pounds, but uncontrollable factors can cause the pressure of individual footballs to vary. For quality control purposes, the manufacturer wishes to estimate the mean inflation pressure to within .025 pounds of its true value with 99 percent confidence. What sample size should be used?

A) 677
B) 107
C) 35
D) 27
E) 11