Product filling weights are normally distributed with a mean of 300 grams and a standard deviation of 15 grams. (a) Develop the control limits for the x chart for a sample of size 10. (Round your answers to two decimal places.) UCL = LCL = Develop the control limits for the x chart for a sample of size 20. (Round your answers to two decimal places.) UCL = LCL = Develop the control limits for the x chart for a sample of size 30. (Round your answers to two decimal places.) UCL = LCL= (b) What happens to the control limits as the sample size is increased? Both control limits come closer to the process mean as the sample size is increased. The UCL comes closer to the process mean and the LCL moves farther from the process mean as the sample size is increased. The LCL comes closer to the process mean and the UCL moves farther from the process mean as the sample size is increased. Both control limits move farther from the process mean as the sample size is increased. The sample size does not affect the control limits. (c) What happens when a Type I error is made? The process will be declared in control and allowed to continue when the process is actually out of The process will be declared out of control and adjusted when the process is actually in control. (d) What happens when a Type II error is made? The process will be declared in control and allowed to continue when the process is actually out of The process will be declared out of control and adjusted when the process is actually in control. (e) What is the probability of a Type I error for a sample of size 10? (Round your answer to four decimal places.) What is the probability of a Type I error for a sample of size 20? (Round your answer to four decimal places.) What is the probability of a Type I error for a sample of size 30? (Round your answer to four decimal places.) (f) What is the advantage of increasing the sample size for control chart purposes? What error probability is reduced as the sample size is increased? Increasing the sample size provides a more accurate estimate of the process mean and reduces the probability of making a Type II error. Increasing the sample size always increases the likelihood that the process is in control and reduces the probability of making a Type II error. Submit Answer ing the sample size provides a more accurate estimate of the process mean and reduces bability of making a Type I error. Increasing the sample size always increases the likelihood that the process is in control and reduces the probability of making a Type I error.