To solve this problem, we need to determine the profit distribution, $X$, for the insurance company, based on whether the woman lives or dies within the one-year policy period.

Step 1: Define Possible Outcomes for Profit $X$

1. If the woman survives (probability = 0.9398):

   • The insurance company only collects the premium, which is $2900.
   • Therefore, the profit $X$ for the company is $2900$.

2. If the woman dies (probability = $1 - 0.9398 = 0.0602$):

   • The insurance company pays $47,000 to her beneficiary.
   • The profit $X$ in this case is $2900 - 47000 = -44100$.

Step 2: Create the Probability Distribution

The probability distribution of $X$, the profit made by the insurance company, is as follows:

• Profit (X) = 2900 with $P(X = 2900) = 0.9398$
• Profit (X) = -44100 with $P(X = -44100) = 0.0602$

So, the distribution is: