A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables. The company collects a premium of $250 each year as payment for the insurance. The amount X that the company earns on this policy is $250 per year, less the $100,000 that it must pay if the insured dies. Here is the distribution of X. Fill in the missing probability in the table and calculate the mean profit μX

To fill in the missing probability in the table, we need to use the information given and the concept of probability.

Based on the given information, the term insurance policy pays $100,000 if the insured dies within the next 5 years. The probability that a randomly chosen male will die each year can be found in mortality tables.

Let's assume that the probability of a 21-year-old male dying within a given year is given as P(year). We'll fill in the probability distribution table using this assumption:

| X | -$99,750 | $250 |
|--------------|------------|-------------|
| Probability | P(Alive) | P(Death) |

Since the policy only pays out if the insured dies, the probability of the insured being alive is 1 - P(Death).

Now, we'll calculate P(Death) for each year using the mortality tables.

To calculate the mean profit μX, we multiply each outcome by its corresponding probability and sum them up. Let's calculate it:

Mean profit μX = (-$99,750 * P(Alive)) + ($250 * P(Death))

Remember that P(Alive) = 1 - P(Death).

That's how you fill in the missing probability in the table and calculate the mean profit μX in this scenario.