2. An industrial sewing machine uses ball bearings that aretargeted to have a diameter of 0.75 inches. The lower and upperspecification limits under which the ball bearings can operateproperly are 0.74 inches and 0.76 inches, respectively.
Past experience has indicated that the actual diameter of theball bearings is approximately normally distributed with a mean of0.753 inches and a standard deviation of 0.004 inches.
What is the probability that a ball bearing is:
a. between the target and the actual mean?
b. between the lower specification limit and the target?
c. above the upper specification limit?
d. below the lower specification limit?
e. Of all the ball bearings, 93% of the diameters are greaterthan what value?
- Document your work clearly and completely. Show your steps
- Use Excel to calculate Z-scores
- Use Appendix Table B.3 Areas Under the Normal Curvefrom your text to find table probabilities.
- Write complete sentences to answer each question. “Theprobability of …. is …..”
