Tool workers are subject to work-related injuries. One disorder, caused by strains to the hands and wrists, is called carpal tunnel syndrome. It strikes as many as 23,000 workers per year. It is estimated that the average cost of this disorder to employers and insurers is approximately $30,000 per injured worker. Suppose these costs are normally distributed, with a standard deviation of $9,000.
a. What proportion of the costs is between $15,000 and $45,000?
b. What proportion of the costs is greater than $50,000?
c. What proportion of the costs is between $5,000 and $20,000?
d. Suppose the standard deviation is unknown, but 90.82% of the costs are more than $7,000. What is the value of the standard deviation?
e. Suppose the mean value is unknown, but the standard deviation is still $9,000. How much is the average cost if 79.95% of the costs are less than $33,000?