Answer:
(a) Yes, he should be worried. The Fatal accident rate (FAR) is too high according to standars of the industry. This chemical plant has a FAR of 167, where in average chemical plants the FAR is about 4.
(b) FAR=167 and Death poer person per year = 0.0033 deaths/year.
(c) The expected number of fatalities on a average chemical plant are one in 12500 years.
Explanation:
Asumming 50 weeks of work, with 40 hours/week, we have 2000 work hours a year.
In 300 years we have 600,000 hours.
With these estimations, we have (1/600,000)=1.67*10^(-6) deaths/hour.
If we have 2000 work hours a year, it is expected 0.0033 deaths/year.
![1.67*10^{-6} \frac{deaths}{hour}*2000 \frac{hours}{year}=0.0033 deaths/year](https://tex.z-dn.net/?f=1.67%2A10%5E%7B-6%7D%20%5Cfrac%7Bdeaths%7D%7Bhour%7D%2A2000%20%5Cfrac%7Bhours%7D%7Byear%7D%3D0.0033%20deaths%2Fyear)
The Fatal accident rate (FAR) can be expressed as the expected number of fatalities in 100 millions hours (10^(8) hours).
In these case we have calculated 1.67*10^(-6) deaths/hour, so we can estimate FAR as:
![FAR=1.67*10^{-6} \frac{deaths}{hour}*10^{8} hours=1.67*10^{2} =167](https://tex.z-dn.net/?f=FAR%3D1.67%2A10%5E%7B-6%7D%20%5Cfrac%7Bdeaths%7D%7Bhour%7D%2A10%5E%7B8%7D%20%20hours%3D1.67%2A10%5E%7B2%7D%20%3D167)
A FAR of 167 is very high compared to the typical chemical plants (FAR=4), so the worker has reasons to be worried.
If we assume FAR=4, as in an average chemical plant, we expect
![4\frac{deaths}{10^{8} hour} *2000\frac{hours}{year}=8*10^{-5} \frac{deaths}{year}](https://tex.z-dn.net/?f=4%5Cfrac%7Bdeaths%7D%7B10%5E%7B8%7D%20hour%7D%20%2A2000%5Cfrac%7Bhours%7D%7Byear%7D%3D8%2A10%5E%7B-5%7D%20%5Cfrac%7Bdeaths%7D%7Byear%7D)
This is equivalent to say
![\frac{1}{8*10^{-5} } \frac{years}{death}=1.25*10^{4} \frac{years}{death} =12500 \, \frac{years}{death}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%2A10%5E%7B-5%7D%20%7D%20%5Cfrac%7Byears%7D%7Bdeath%7D%3D1.25%2A10%5E%7B4%7D%20%5Cfrac%7Byears%7D%7Bdeath%7D%20%3D12500%20%5C%2C%20%5Cfrac%7Byears%7D%7Bdeath%7D)
The expected number of fatalities on a average chemical plant are one in 12500 years.