1) Suppose that the specification limits for diameters of bolts are 82 to 118 mm. Suppose that the diameters of individual bolts follow a Normal distribution with a mean of 100 mm. and a standard deviation of 6 mm.

What is the probabilty that the diameter of a bolt is within specs?

Suppose that the manufacturer manages to improve the process so that the standard deviation is reduced to only 3 mm. But suppose that the mean of the process has slipped up to 109 mm. What proportion of diameters will now be expected to exceed the upper specification limit ?

2) Treat the nine digits 6, 5, 1, 3, 7, 4, 4, 8, 0 as a sample.

- Compute the sum of squares.

- Compute the sum of squared deviations SSD using the computational formula SSD = Sum of squares - Sum²/n.

- Compute the sample variance.