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?
Many lakes are carefully monitored for pH concentration, total phosphorus, chlorophyll, nitrogen, and total suspended solids. These data are used to characterize the condition of the lake and to chart year-to-year variability. Based on information from the Lake Partner Program, Ontario Ministry of the Environment, Aberdeen Lake has a mean total phosphorus concentration of 14.6 mg/liter and standard deviation 5.8 mg/liter. Suppose a day is selected at random, and a total phosphorus measure from Aberdeen Lake is obtained.
a. What is the probability that the total phosphorus is less than 13 mg/liter?
b. What is the probability that the total phosphorus differs from the mean by more than 5 mg/liter?
c. Suppose the total phosphorus is less than 20 mg/liter. What is the probability that it is less than 14 mg/liter?
d. If the total phosphorus measurement is 27 mg/liter, is there any evidence to suggest the mean has increased?