The diameters of ball bearings manufactured by a process are normally distributed with mean of 4.52 cm and standard deviation of 0.04 cm. The specification for the diameter of a bolt is 4.50 ± 0.05cm.
1. What proportion of the ball bearings manufactured by this process meet the specifications?
2. What is the 99th percentile of the diameter of the ball bearing?
3. If the mean is set to 4.50 cm instead of 4.52 cm through calibration, what proportion of the ball bearings will meet specifications?
4. If the mean is set to 4.50 cm, what must the standard deviation be so that 99% of the ball bearings will meet specifications?