mean 1.15 standard deviation 2.2 sharp .30 assuming fund returns are normally distributed, the probability that the monthly return is less than -3.25 is closest to… a- .025 b- .050 c- .150 d- .30 how do we do this?
A -3.25 is 2 STD away from the mean. 95% of returns will fall between 1.15± 2std, 5% won’t. since you are only looking for 1 tail (less than 2s), it is 2.5%
yup… i cant fgure this out for some reason
answer is A… just what Long said… imagine what a normal distribution looks like… the mean is 1.15… 2 standard devs from the mean is the range -3.25 to 5.55… now, if you shade that area, thats 95% of the graph… which means there must be 5% left in the tails… but you only want one of the tails, so, half of 5% is 2.5% (the good thing about normal distributions is its symmetry, so everything is easy to work out)
got it … drawing the picture in my head helps… where i really get messed up is when construcing CI… i hate these… quant aint my thing… like for example… in this problem how do you know to 95 ci as 2 standard deviations… as opposed to 95 ci being 1.96 standard deviations…
ahhhh i also get mixed up with the exact same thing… i asked my mate (who’s a statistics tutor at uni) and he pretty much said: if you are estimating a POINT, then use the usual standard deviation… if you are estimating an AVERAGE, then use the standard error… since averages have less variation than single points, this variance must be scaled by the sample size… but now im thinking, i totally didnt answer your question did i? hehe sorry… pretty much, to answer your question, 2 is roughly equal to 1.96
i just dont grasp this 2 well… i always mess up when to use ci and just the regular distribution
well, lets say you were to use 1.96 instead of 2… your answer still would have been A. While not exactly 0.025, it would have been close.
another thing, what i tell my students is, to draw out a huge normal distribution… draw in vertical lines for the mean… 1,2,and 3 standard deviations away… now, work out (using the basic rules, and symmetry) what each segment of the graph will be (in percentage terms)
(-3.25 - 1.15) / 2.2 = -2 P( z < -2 ) = .025 given 2sigma is approx 2. and 2 sigma 2 tailed = 95%
yup… I find it much easier to tackle these problems in the same way that cpk did above… definitely makes it more straightforward
it is just tat the problem did not give me a z table… so going that route was not an option