Tool workers are subject to work-related injuries. One disorder, caused by strai
ID: 3174810 • Letter: T
Question
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. 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. What proportion of the costs are between $15,000 and $45,000? What proportion of the costs are greater than $50,000? What proportion of the costs are between $5,000 and $20,000? 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? 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?Explanation / Answer
a. From information given, mu=30,000, sigma=9000. Substitute the values in following z score formula to compute z scores for x1=15,000 and x2=45,000. The z score formula is:z=(X-mu)/sigma, where, X is raw score, mu is population mean, sigma is population standard deviation.
z1=(15000-30000)/9000=-1.67 and z2=(45000-30000)/9000=1.67
the two z scores are of opposite signs, therefore, find areas between mean and respective z scores and add them.
P(15000<X<45000)=0.4525+0.4525=0.905 (ans)
b. P(X>50000)==1-P(X<=50000)=1-P[Z<=(50000-30000)/9000]=1-P(Z<=2.22)=1-0.9868=0.0132 (ans)
c. z1=-2.78, z2=-1.11. The two z scores are of same sign, therefore, find area between mean and respective z scores and subtract the smaller area from the larger one.
P(5000<X<20000)=0.4973-0.3665=0.1308 (ans)
d. P(X>7000)=0.9082 can be reexpressed as follows:
1-P(X<=7000)=0.9082
P(X<=7000)=1-0.9082=0.0918
The Z score corresponding to area 0.0918 is -1.33.
Substitute the value in z score formula to compute sigma.
-1.33=(7000-30000)/sigma
-1.33=-23000/sigma
sigma=17293.2~17293 (ans)