Please verify if I made mistakes.

4. A process filling small bottles with baby formula has a target of 3 ounces +/- 0.140 ounces. Two hundred bottles from the process were sampled. The results showed the average amount of formula placed in the bottles to be 3.044 ounces. The standard deviation of the amounts was 0.035 ounce.

1. Determine the Cpk value of the process.

3+0.140=3.140 is upper limit (USL)

3-0.140 =2.86 (LSL)

Cpk= min(Cpu,Cpl)

Cpl = (Process Mean - LSL)/(3*Standard Deviation)

Cpu = (USL - Process Mean)/(3*Standard Deviation)

Cpu=(3.044-2.86)/(3*0.035)=1.75

Cpl=(3.14-3.044)/(3*0.035)=0.91

Cpk = 0.91.

2. Roughly what proportion of bottles meet the specifications (research required)?

Zusl=(Usl-Mean)/standard deviation

Zlsl=(Mean-Lsl)/Standard deviation

Zusl=2.74

ZLsl=(3.044-2.86)/0.035=5.25

Z table value of 2.74

2.74 gives 0.0031.

0.0031*100=0.31% of bottles lie outside the USL.

Zlsl=5.25 and any value greater than Z=4 will give 0.

Total proportion of bottles outside the specifications is 0.31% + 0% = 0.31%

100- 0.31=99.69%