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.

*(Round the values of z to 2 decimal places, e.g. 0.12. Round your answer to 3 decimal places, e.g. 0.122.)

**(Round the values of z to 2 decimal places, e.g. 0.12. Round your answers to 4 decimal places, e.g. 0.1234.)

(a)What proportion of the costs are between $15,000 and $45,000?

enter proportion rounded to 4 decimal places

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

enter proportion rounded to 4 decimal places

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(c)What proportion of the costs are between $5,000 and $20,000?

enter proportion rounded to 4 decimal places

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(d)Suppose the standard deviation is unknown, but the mean is still $30,000 and 90.82% of the costs are more than $7,000. What would be the value of the standard deviation?

enter the standard deviation rounded to 3 decimal places

*

(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? $

enter a dollar amount