Answer:
Explanation:
From the information given:
Total defectives = 87
Total observations = 1600
At 95% confidence interval;
critical value [tex]Z_{0.025}[/tex] = 1.96
Proportion (P) of defect = total defectives/total observations
P = 87/1600 = 0.0544
Since: P + Q = 1
Q = 1 - P
Q = 1 - 0.0544
Q = 0.9456
The average sample size = 100
Standard deviation [tex]S_p =\sqrt{ \dfrac{P*Q}{N}[/tex]
[tex]S_p =\sqrt{ \dfrac{0.0544\times 0.9456}{100}}[/tex]
[tex]\mathbf{S_p = 0.02270}[/tex]
The upper control limit UCL = [tex]P+ (z_{0.025} \times S_p)[/tex]
= 0.0544 + (1.96 × 0.02270)
= 0.098892
The lower control limit LCL = [tex]P - (z_{0.025} \times S_p)[/tex]
= 0.0544 - (1.96 × 0.02270)
= 0.009908
