Medicine and Clinical Studies Repeated industrial tasks often cause work-related muscle disorders. Measurements of joint angles (of the shoulder and elbow, for example) required to complete a certain task can be used to predict future injuries. The shoulder joint angle required to fasten an aluminum door frame on an assembly line varies according to the worker's height, arm length, and location. The shoulder joint angle for this task is normally distributed with mean 23.7 degrees and standard deviation 1.9 degrees. Suppose an employee is randomly selected.
a. What is the probability that the shoulder joint angle will be between 20 and 25 degrees?
b. What is the probability that the joint angle will be less than 18 degrees?
c. If the joint angle is more than 28 degrees, there is a good chance the employee will suffer from a muscle disorder. What is the probability that the employee will suffer from a muscle disorder?
d. If the joint angle is between 21.7 and 25.7 degrees, then management believes the ergonomics of the task are adequate. If five employees are randomly selected, what is the probability that four of the five have adequate ergonomics?