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 = 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 3σX is called a process
control chart.)