Question 1 (20 marks) A common method for measuring the size of a listed company is to use its market capitalization, which is computed by multiplying the number of stock shares by the price of a share of stock. The entire population of market capitalization values is known to follow the normal distribution with 2.28% of the companies over 900 billion and 15.87% of the companies below 300 billion. (a) Find the mean and standard deviation of the population distribution. (7 marks) (b) An investment portfolio is formed by randomly selecting 16 listed companies. Find the probability that the total market capitalization value of the selected companies is over 6400 billion. (5 marks) (c) Two investment portfolios have been formed, each of which consisting of ten randomly selected listed companies whose market capitalizations in billion are tabulated below. Portfolio 1 370 558 385 345 219 507 675 488 322 234 Portfolio 2 667 620 166 683 599 204 613 451 331 339 By considering the median and the range only, compare the central tendency and variation of the two portfolios. (8 marks) Question 2 (10 marks) Two mutual funds, (I) and (II), have independent yearly performance over the next five years. Fund (I) and fund (II) have constant probability of 0.6 and 0.7 of growth in any one year, respectively. (a) Explain which one of the two mutual funds has a higher expected growth over the next five years. (4 marks) (b) Explain which one of the two mutual funds has yearly growths which are more spread out over the next five years. (4 marks) (c) Find the probability that fund (I) records three years of growth at the end of the fifth year. (2 marks)
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