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$)?$