The manufacture of official NFL footballs uses a machine to

The manufacture of official NFL footballs uses a machine to inflate its new balls to a pressure of 13.5 pounds. When the machine is properly calibrated, the mean inflation pressure is 13.5 pounds, but uncontrollable factors cause the pressures of individual footballs to vary randomly from about 13.3 to 13.7 pounds. For quality-control purposes, the manufacture wishes to estimate the mean inflation pressure to within .025 pound of its true value with a 99 percentage confidence interval. What sample size should be used?

Solution

take standard deviation as range/4,SD= (13.7-13.3)/4=0.1

Sampling error SE=0.025

100(1-a)=99

a=0.01

a/2=0.005

calculate z corresponding to 0.005

then n= z*SD^2/SE^2

n comes around 110.