Answer:
The expected cost of the company for a 3000 tires batch is $120255
Step-by-step explanation:
Recall that given a probability of defective tires p, we can model the number of defective tires as a binomial random variable. For 3000 tires, if we have a probability p of having a defective tire, the expected number of defective tires is 3000p.
Let X be the number of defective tires. We can use the total expectation theorem, as follows: if there are events that partition the whole sample space, and we have a random variable X over the sample space, then
.
So, in this case, we have the following
.
Let Y be the number non defective tires. then X+Y = 3000. So Y = 3000-X. Then E(Y) = 3000-E(X). Then, E(Y) = 2949.
Finally, note that the cost of the batch would be 40Y+45X. Then