so i got a answer from an expert and checked with online bot they gave me two different answers could you please see which one is correct and i should use.

here is the question:

A financial investor builds a portfolio that is worth an expected $35$mil. The investor knows that his analysts can build a model to boost the potential return from the portfolio investment. The additional return has a Normal Distribution with mean $3$mil and standard deviation $0\mathrm{.}5$mil. The investor wishes to sell his financial services at a price that guarantees his expected profit will be $5\%$ of the total return from the portfolio.

$1)$ Simulate $($with a min of $200$ repetitions$)$ the average and the standard deviation of the profit the financial advisor realizes when setting the price for his services between $1\%$ and $10\%$ of the total expected return from the portfolio. Then discuss your findings. $$

here is the answer the expert gave me:

Calculate the averages and standard deviations of the profits for prices between $1\%$ and $10\%$ of the portfolio's total expected return of $38$ million.

Price $(\%$ of portfolio return$)|$ Average Profit $($mil$)|$ Standard Deviation $($mil$)$

$1\%|0\mathrm{.}8|0\mathrm{.}191$

$2\%|1\mathrm{.}3|0\mathrm{.}245$

$3\%|1\mathrm{.}8|0\mathrm{.}288$

$4\%|2\mathrm{.}3|0\mathrm{.}327$

$5\%|2\mathrm{.}8|0\mathrm{.}362$

$6\%|3\mathrm{.}3|0\mathrm{.}393$

$7\%|3\mathrm{.}8|0\mathrm{.}421$

$8\%|4\mathrm{.}3|0\mathrm{.}446$

$9\%|4\mathrm{.}8|0\mathrm{.}468$

$10\%|5\mathrm{.}3|0\mathrm{.}487$

These findings show that the average profit rises in tandem with the price of the financial service, which makes sense given that the investor keeps a bigger share of the total return. But the standard deviation also rises, indicating a greater degree of unpredictability or risk related to the profits.

As a result, the investor must find a way to balance the need to set a higher price in order to maximise profit with the need to make sure that the risk involved in the variability of profits is reasonable. When determining the cost of financial services, other elements like the value proposition, clientele, and level of competition should also be taken into account.

Below is anther answer that i got from a bot which says that above is wroung:

To verify if your analysis and conclusions are correct, I'll run another simulation based on the parameters and the profit calculation you've outlined. We'll check whether the average profits and standard deviations for each percentage from $1\%$ to $10\%$ of the total expected return align with your results. Then, we can confirm whether the trend of increasing profit and standard deviation with higher pricing percentages holds as per your findings.

We will again use:

Portfolio value: $35$ million

Mean of additional return: $3$ million

Standard deviation of additional return: $0\mathrm{.}5$ million

Total expected return: $38$ million

Let's proceed with the simulation for each price point from $1\%$ to $10\%$ of $38$ million, calculate the average profit, and standard deviation, then compare to your table.

The simulation results show a significant deviation from the table you provided. Here's a summary of our simulated results:

Price $(\%$ of portfolio return$)$ Average Profit $($mil$)$ Standard Deviation $($mil$)$

$1\%2\mathrm{.}70\mathrm{.}511$

$2\%2\mathrm{.}20\mathrm{.}472$

$3\%1\mathrm{.}80\mathrm{.}516$

$4\%1\mathrm{.}40\mathrm{.}486$

$5\%1\mathrm{.}10\mathrm{.}470$

$6\%0\mathrm{.}80\mathrm{.}461$

$7\%0\mathrm{.}30\mathrm{.}483$

$8\%0\mathrm{.}00\mathrm{.}502$

$9\%-0\mathrm{.}40\mathrm{.}504$

$10\%-0\mathrm{.}80\mathrm{.}465$

Key Observations:

As the price percentage increases from $1\%$ to $10\%,$ the average profit initially decreases from $2\mathrm{.}7$ to $0\mathrm{.}8$ million, and then becomes negative. This is different from your results where the average profit continuously increases as the percentage price increases.

Standard deviations are generally around $0\mathrm{.}5$ million, showing some level of variability but not dramatically increasing with the price as suggested in your table.

Conclusion:

The findings from the simulation suggest a different trend compared to what was indicated in your answer. Instead of profits increasing with higher price percentages, profits actually decrease and become negative as the price surpasses the additional return's mean $(3$ million$),$ reflecting the diminishing returns and the set prices cutting into the potential profit.

The original answer's assertion that profits increase as the pricing percentage increases does not align with our simulations, which may be due to assumptions about the variability and distribution of the additional returns, or a misunderstanding of how the price affects net profits when additional returns are normally distributed with a fixed mean an