chetan86

OK - messed up thread....

0) We have wittgenstein commenting on mathematics and everyone knows that is just to honk off Bertrand Russell and all other real mathematicians.

1) The first problem is bogus, so if you are having trouble with it, it might be because the problem stinks. The real answer is E) unknown because we dont know anything about the distribution of time it takes a passenger to reach the boarding gate after arrival. The calculation in the answer assumes that it is normally distributed. That doesn't sound likely to me and would surely need to be stated (for one thing it has a minimum which is something like the time it would take Usain Bolt to cover the distance unimpeded by security gates and what-not - like OJ in the old Avis commercials that you are all too young to remember).

2) Rus1Bus is on the right track, but his explanation is a little messed.

To fix up the example - forget about a finite or known sized population, except to assume that it is much bigger than the sample size. The standard deviation is always much smaller than the range of the data. In a normal population of size 1000, the standard deviation will be something like 1/5 or 1/6 of the range so the standard deviation here would be something like 5 or 6, not 30.

So now we take samples of size 100 from the population and take the mean of each sample. The samples are randomly chosen, so the sample means are random. If they are random, they have a distribution called the sampling distribution. Some math or some careful though says that if the sample has a standard deviation, then the sampling distribution has a standard deviation. Then some math or a carfeul look at the CFA notes says that the standard deviation of the sampling distribution is (sd of sample)/sqrt(sample size). That's the standard error. The really cool thing is that the sampling distribution is normally distributed "regardless" of the distribution of the ages of the candidates - the central limit theorem. That means that standard error is really valuable for deciding how close your sample mean is likely to be to the actual unknown population mean.

The known vs unknown sd is not much of an issue. When would you ever know the population sd but not know the population mean? (only when some oracle of a problem writer tells you)