Toolworkers 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. The U.S. Labor Department estimates 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 are between $15,000 and $45,000?

b. What proportion of the costs are greater than $50,000?

c. What proportion of the costs are 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 would be the value of the standard deviation?

e. Suppose the mean value is unknown, but the standard deviation is still $9,000. How much would the average cost be if 79.95% of the costs were less than $33,000?