Question 2: The thickness (mm) of the coating applied to disk drives
is a characteristic that determines the usefulness of the product. When no
unusual circumstances are present, the thickness X has a normal distribution
with mean µ = 3 mm and standard deviation σ = .05 mm. Suppose that the
coating process will be monitored by selecting a random sample of 16 drives
from each shift’s production and determining X¯, the sample mean coating.
(a) (3 marks). Describe the sampling distribution of X¯.
(b) (1 mark). When no unusual circumstances are present, we expect X¯ to
be within 3σX¯ of 3 mm, the desired coating thickness value. A value of
X¯ farther from 3 than 3σX¯ is interpreted as an indication of a problem
that needs attention. Compute 3 ± 3σX¯. (A plot over time of values of
X¯ with horizontal lines drawn at the limits µ ± 3σX¯ is called a process
control chart.)