Someone please make me understand the solution of these questions.

纳Part 1After 72 FRM Part 1 students took a mock exam, the mean score was 75. Assuming that the population standard deviation is 10, construct a 99% confidence interval for the mean score on the mock exam. A (75, 85) B (65, 75) C (71.96, 78.04) D (75, 78.04) The correct answer is: C A 99% CI for the mean, μ = x̄ ± Zα/2 *σ/√n where α =0.01From the normal dist. table, Z0.005 = 2.58μ = 75 ± 2.58 * 10/√72= 75 ± 3.04Giving us a CI = 71.96 ≤ μ ≤ 78.04 *User Question: Please when do we have to use 1,96 for the normal distribution instead of using the normal dist tabke?

纳Part 1A company pays a dividend of $100,000 quarterly forever starting from now. Assume an annual nominal rate of interest of 4%. Calculate the present value of the dividends. A $9,000,000 B $9,100,000 C $10,100,000 D $11,100,000 E $11,200,000 This is perpetuity-due: $$ \cfrac {100000}{d}= \cfrac {100000(1+i)}{i}=10,100,000 $$ *User Question: could help to put in the solution why the interest rate is 1% and not 4% (its because it's quarterly and so you would divide the i by 4 and then you multiply by (1+i) because its a perpetuity due)

Actuarial - FM(Financial Mathematics)对冲基金已经开始一年37美元的价值0 million and a 2 plus 20 fee structure with no hurdle rate or watermark. The hedge fund structure is set up such that the management fee is calculated on the assets at the beginning of the year and that the incentive fee is calculated net of the management fee. If the fund's ending value is $400 million, then what are the total fees paid to the hedge fund for the period? A $12.4 million. B $11.92 million. C $16 million. D $4.4 million. The correct answer is: B Management fee = $370 million * 2% = $7.4 million Incentive fee = ($400 million - $7.4 million - $370 million) * 20%= $4.52 million Total fees = Management fee + Incentive fee = $7.4 million + $4.52 million = $11.92 million *User Question: Given that the Management Fee was paid at the beginning of the year, then then the Fund NAV at the year-end is already net of the Management Fee. Doesn't then deducting The Management Fee again from the Performance Fee amount results in double counting?

纳Part 1How dependent on the particular circumstances (i.e., context) are machine learning approaches within the financial services sector? A Not dependent at all B Dependent to a smaller degree C Dependent to a significant degree D Highly dependent The correct answer is: D The application of machine learning approaches within the financial services sector is highly context-dependent. *User Question: Pardon me, as a non-English speaker, I'm quite confuse the difference between significant and highly, they seem the same for me, is anyone could expalin, please

纳Part 2