Wasserman and wadsworth 1989 discuss a process for the manufacture of steel bolts that continuously feed an assembly line downstream. Historically, the thickness of these bolts follow a normal distribution with a mean of 10.0 mm and a standard deviation of 1.6 mm. Process supervision becomes concerned about the process if the thickness begin to get larger than 10.8 mm or smaller than 9.2 mm. Assume that the current process mean is 10.0 mm, and consider a randomly selected bolt.
a. Find the probability that the thickness of this bolt is between 9.2 and 10.8 mm.
b. Find the probablility that the thickness of this bolt is smaller thn 9.2mm