In a manufacturing facility, a specific machine produces cylindrical components, andthe diameter of these components follows a normal distribution with a mean diam-eter of 50 millimeters and a standard deviation of 2 millimeters. Quality controlmeasures are in place to ensure that most components meet the required specifica-tions.

(a) Calculate the probability that a randomly selected component has a diameterbetween 48 and 52 millimeters.

(b) The company has strict quality standards, and components with diametersless than 48 millimeters or greater than 52 millimeters are considered defects.What is the probability of a randomly selected component being a defect?

(c) To optimize production, the company wants to produce components with adiameter greater than 52 millimeters. What percentage of components meetthis requirement?

(d) If the company wants to introduce a new quality control threshold at 51 mil-limeters, what is the minimum percentage of components that should meet thisthreshold to maintain a high level of quality (i.e., less than 5% defective)?