Answer:
The process does not meets the specifications.
Step-by-step explanation:
It is provided that the Crunchy Potato Chip Company packages potato chips in a process designed for 10.0 ounces of chips.
The value of upper specification limit is, USL = 10.5 ounces.
The value of lower specification limit is, LSL = 9.5 ounces.
The mean weight of the chips bags is, [tex]\bar X=9.8\ ounces[/tex].
And the standard deviation weight of the chips bags is, [tex]\sigma=0.12\ ounces[/tex].
Compute the value of process capability as follows:
[tex]C_{p_{k}}=min \{C_{p_{L}},\ C_{p_{U}}\}[/tex]
Compute the value of [tex]C_{p_{L}}[/tex] as follows:
[tex]C_{p_{L}}=\frac{\bar X-LSL}{3 \sigma}=\frac{9.8-9.5}{3\times 0.12}=0.833[/tex]
Compute the value of [tex]C_{p_{K}}[/tex] as follows:
[tex]C_{p_{K}}=\frac{USL-\bar X}{3 \sigma}=\frac{10.5-9.8}{3\times 0.12}=1.944[/tex]
The value of process capability is:
[tex]C_{p_{k}}=min \{C_{p_{L}},\ C_{p_{U}}\}[/tex]
[tex]=min\{0.833,\ 1.944\}\\=0.833[/tex]
The value of process capability lies in the interval 0 to 1. So the process is not capable of meeting design specifications.
Thus, the process does not meets the specifications.
