Final answer:
Widening the distance between the control limits on a mean chart decreases the producer's risk, which is the risk of incorrectly rejecting products that meet quality standards, thus reducing the likelihood of a Type I error.
Step-by-step explanation:
When considering the question of whether widening the distance between the control limits on a mean chart will increase or decrease the producer's risk, it's important to understand that control limits are thresholds in quality control charts used to determine whether a process is in statistical control.
In this case, increasing the distance between control limits makes them wider, which would typically decrease the likelihood of a Type I error (false alarm), where a product is incorrectly identified as being out of specification when it actually meets the standards.
This means that by widening the control limits, the producer's risk of incorrectly rejecting good products is reduced. However, this comes at the expense of increasing the likelihood of a Type II error (miss), where a defective product is not identified and is incorrectly accepted as meeting the specifications.