Question

the occupational safety and health administration (osha) has determined that the probability of a worker dying from exposure to a hazardous chemical used in the production of fertilizer is 0.008. the cost of imposing a regulation that would ban the chemical is $31 million. if the value of a human life is equal to $8 million, how many people must the policy affect in order for the benefits to exceed the costs? 248 485 3,101 3,876

Explanation:

Step1: Set up the inequality

Let \(n\) be the number of people. The benefit is the value of a life times the probability of saving a life times the number of people, i.e., \(8\times0.008n\). The cost is \(31\). We want \(8\times0.008n>31\).

Step2: Solve the inequality

First, calculate \(8\times0.008 = 0.064\). So the inequality becomes \(0.064n>31\). Then, solve for \(n\) by dividing both sides by \(0.064\): \(n>\frac{31}{0.064}\).
\(\frac{31}{0.064}=\frac{31\times1000}{64}=\frac{31000}{64} = 484.375\). Since \(n\) represents the number of people, and it must be an integer, we round up.

Answer:

\(485\)