Okay, I can understand the solution as given below. However, I approached the question using Chebysev’s theorem. My approach was as follows: 350-280 = 70 which is approximately 2 standard deviations away from the mean. Now, 1/k^2 = 1/2^2 = 1/4 = .25 .25/2 = .125 = 12.5% is the answer. Where did I mess up? Thanks all. A study of hedge fund investors found that their household incomes are normally distributed with a mean of $280,000 and a standard deviation of $40,000. The percentage of hedge fund investors that have incomes greater than $350,000 is closest to: A) 5.0%. B) 25.0%. C) 3.0%. D) 4.0%. Your answer: B was incorrect. The correct answer was D) 4.0%. z = (350,000 – 280,000)/40,000 = 1.75. Using the z-table, F(1.75) = 0.9599. So, the percentage greater than $350,000 = (1 – 0.9599) = 4.0%. The percentage of hedge fund investors with income less than $180,000 is closest to: A) 1.15%. B) 0.62%. C) 2.50%. D) 6.48%. Your answer: D was incorrect. The correct answer was B) 0.62%. z = (180,000 – 280,000)/40,000 = –2.50. Using the z-table, F(–2.50) = (1 – 0.9938) = 0.62%.

if i remember correctly , chebyshev’s theorm gives an approximation for any probability distribution. But that’s where it ends - to arrive at a solid number, you should use those z tables like the solution does.

Whoa - Chebyshev gives you bounds for any distribution (come to think of it, I’m not sure what distributions if any achieve the Chebyshev bounds although it seems like something I should know). Once they tell you that you have a normal distribution, you have vastly more information than in any problem where you use Chebyshev. You have a completely specified distribution and instead of saying that “at least 3/4 of the distribution lies with 2 s.d. of the mean” you can say “exactly 95.[whatever] % of the distribution ies within 2 s.d. s of the mean” where [whatever] can be 5 billion decimal places and counting…

As Taleb says, the normal distribution is an idiotic distribution invented for Mickey Mouse economic theories back in the day, lol.

He just says that to get a rise out of people but doesn’t even believe it himself.

sublimity Wrote: ------------------------------------------------------- > As Taleb says, the normal distribution is an > idiotic distribution invented for Mickey Mouse > economic theories back in the day, lol. hence LTCM blew up. they were wrong in the VAR estimates – but VAR wont work for Hedge funds b/c HF rtns are NOT normally distributed. Most have a negative skew, meaning huge negative event risk…

JoeyDVivre Wrote: ------------------------------------------------------- > He just says that to get a rise out of people but > doesn’t even believe it himself. Ah, in that case, then that reminds me of S.L. of Freakonomics (and other books like it, where very strong, ebullient, overconfident assertions are made in order to get a strong reaction). All I remember from reading that allegedly deep book was: 1. Cool little twists in thoughts and common situations, though nothing too fundamentally and theoretically descriptive or predictive. The ideas in Freakonomics are book-selling ideas…but whatever, I ended the book with: *shrug*, cool, what are the next five books I can read to kill some time? 2. A ridiculous introduction where S.L. is described as the new messiah. IMO, he’ll still be a few cuts below von Neumann, Einstein, and Bohr even if everyone in the world helps that book stay on the NY Times bestseller for a while and he wins an Economics Nobel prize (or two).