Toolworkers are subject to work-related injuries. One disorder, caused by strain
ID: 2934201 • Letter: T
Question
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. Round your answer to 3 decimal places.)
**(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)
(a) What proportion of the costs are between $15,000 and $45,000? **
(c) What proportion of the costs are between $5,000 and $20,000? **
Explanation / Answer
Mean = $30,000
Standard deviation = $9000
P(X < A) = P(Z > (A - mean) / standard deviation)
A) P($15000 < X < 45000) = P(X < 45000) - P(X < 15000)
= P(Z < (45000 - 30000)/9000) - P(Z < (15000 - 30000)/9000)
= P(Z < 1.67) - P(Z < - 1.67)
= 0.9525 - 0.0475
= 0.9050
C) Proportion of cost between 5000 and 2000 = P(X < 20000) - P(X < 5000)
= P(Z < (20000-30000)/9000) - P(Z < (5000 - 30000)/9000)
= P(Z < -1.11) - P(Z < - 2.78)
= 0.1357 - 0.0027
= 0.1330
D) Let the standard deviation be S
P(X > 7000) = 0.9082
P(X < 7000) = 0.0918
P(Z < (7000-30000)/S) = 0.0918
(7000 - 30000)/S = -1.33
S = 17293.233