Part 2 of 2 The defect rate for your product has historically been about \( 1.00 \% \). For a sample size of 100, the upper and lower 3-sigma control chart limits are: 8 of \( 8 \mid \) My score: \( 6.83 / 8 \) pts ( \( 85.34 \% \) ) \( U C L_{p}=0.0399 \) (enter your response as a number between 0 and 1, rounded to four decimal places). \( L C L_{p}=\square \) (enter your response as a number between 0 and 1, rounded to four decimal places).

To find the control chart limits, we first need to understand how to compute the Upper Control Limit (UCL) and Lower Control Limit (LCL) for a defect rate. Given that the defect rate is approximately \( P = 0.01 \) (or 1%), and the sample size \( n = 100 \), we can calculate the control limits using the formula: \[ UCL = P + 3 \sqrt{\frac{P(1-P)}{n}} \] \[ LCL = P - 3 \sqrt{\frac{P(1-P)}{n}} \] Calculating \( UCL \): \[ UCL = 0.01 + 3 \sqrt{\frac{0.01(1-0.01)}{100}} = 0.01 + 3 \sqrt{\frac{0.01 \times 0.99}{100}} = 0.01 + 3 \sqrt{0.00099} \approx 0.01 + 0.0597 = 0.0697 \] So, rounded to four decimal places, \( UCL_{p} = 0.0697 \). Now calculating \( LCL \): \[ LCL = 0.01 - 3 \sqrt{\frac{0.01(1-0.01)}{100}} = 0.01 - 3 \sqrt{0.00099} \approx 0.01 - 0.0597 = -0.0497 \] Since negative proportions are not meaningful in this context, we truncate it to \( LCL = 0 \). Thus, your responses should be: - \( UCL_{p} = 0.0697 \) - \( LCL_{p} = 0.0000 \) (as a rounded number between 0 and 1).