Step 1 :The expected value of a random variable is the long-term average or mean value. It is the sum of all possible values each multiplied by the probability of its occurrence.
Step 2 :In this case, the insurance company either makes a profit of $190 (the cost of the policy) if the female survives the year, or it loses $270,000 - $190 = $269,810 if the female does not survive the year.
Step 3 :The probabilities of these events are given as 0.999544 and 1 - 0.999544 = 0.000456 respectively.
Step 4 :We can calculate the expected value by multiplying each outcome by its probability and summing these products. The outcomes are $190 and -$269810, and the probabilities are 0.999544 and 0.000456 respectively.
Step 5 :The expected value of the policy to the insurance company is approximately $66.88. This means that, on average, the insurance company expects to make a profit of $66.88 on every 20-year-old female it insures for 1 year.
Step 6 :This is the long-term average profit the company expects to make per policy sold to a 20-year-old female, taking into account both the probability of the female surviving the year and the probability of her not surviving the year.
Step 7 :Final Answer: The correct interpretation of the expected value is that the insurance company expects to make a profit of \(\boxed{66.88}\) on every 20 -year-old female it insures for 1 year.