A teller at a drive-up window at a bank had the following service times (in minutes) for 20 randomly
selected customers.
SAMPLE
1 2 3 4
4.5 4.6 4.5 4.7
4.2 4.5 4.6 4.6
4.2 4.4 4.4 4.8
4.3 4.7 4.4 4.5
4.3 4.3 4.6 4.9
a. Determine the mean of each sample.
b. If the process parameters are unknown, estimate its mean and standard deviation.
c. Estimate the mean and standard deviation of the sampling distribution.
d. What would three-sigma control limits for the process be? What alpha risk would they provide?
e. What alpha risk would control limits of 4.14 and 4.86 provide?
f. Using limits of 4.14 and 4.86, are any sample means beyond the control limits? If so, which one(s)?
g. Construct control charts for means and ranges using Table 10.3. Are any samples beyond the
control limits? If so, which one(s)?
h. Explain why the control limits are different for means in parts d and g.
i. If the process has a known mean of 4.4 and a known standard deviation of .18, what would
three-sigma control limits be for a mean chart? Are any sample means beyond the control
limits? If so, which one(s)?