Problem 2 (15 points)
Samples of size
�
=
5
n=5 are collected from a process every half hour. After 50 samples have been collected, we calculate
�
ˉ
=
20.0
X
ˉ
=20.0 and
�
ˉ
=
1.5
S
ˉ
=1.5. Assume that both charts exhibit control and that the quality characteristic is normally distributed.

(a) Estimate the process standard deviation.

(b) Find the control limits on the
�
ˉ
X
ˉ
and
�
S charts.

(c) If the process mean shifts to 22, what is the probability of concluding that the process is still in control?