QUANT Q standard, investment, expected, exceeding

simeezee

I cant' seem to get any of these type of quant questions for the life of me!!!! PLEASE HELP!!!

PLEASE EXPLAIN THESE TYPES OF QUESTIONS



A group of investors wants to be sure to always earn at least a 5% rate of return on their investments. They are looking at an investment that has a normally distributed probability distribution with an expected rate of return of 10% and a standard deviation of 5%. The probability of meeting or exceeding the investors' desired return in any given year is closest to:

A) 34%.

B) 98%.

C) 84%.


Answer is C

The mean is 10% and the standard deviation is 5%. You want to know the probability of a return 5% or better. 10% - 5% = 5% , so 5% is one standard deviation less than the mean. Thirty-four percent of the observations are between the mean and one standard deviation on the down side. Fifty percent of the observations are greater than the mean. So the probability of a return 5% or higher is 34% + 50% = 84%.

PLEASE EXPLAIN THESE TYPES OF QUESTIONS

soddy1979

I like thinking about the normal distribution graph when I think of these questions:

Picture the graph - these percentages encompass

68%: +/- 1 SD
95%: +/- 2 SD
99%: +/- 3 SD

So this question basically says you can go 1 SD below the mean. Thus, the entire upper half of the distribution (50%) is okay, and ONE (1) SD below is fine (half of 68%).

If you segment 6 pieces of the normal distribution, the right-most 4 distributions ( from -1 to 3 SDs) are encompassed.

I don't know how helpful this may be for you, this is just how I think of how to do these types...

hariRaj

is this right?

10 - 5/5 = 1 = .68

1 - .68 = .32

.32/2 = .16

1 - .16 = .84

C

nitoha

Here's my take of the question - whenever you see the question saying it is normally distributed, that means you know you need to calculate the z-score. It's just:

z = (X - mu) / sigma = (5 - 10) / 5 = -1.

So you know that 68% falls within your +/- 1 std dev (away from mean). The answer must be larger than 68%. You also know that if 68% falls within +/- 1 std dev, then 1 - 0.68 = 0.32 (or 32%) must fall under the 2 tails.

Since you're only interested in >5, (the right tail), simply half the 32% and add that back to your original 68% and you're done. It's easier to understand, imo, if you just do 68% + 32%, instead of 34% + 50%.

I find it easier to understand, by picturing it on a bell-shaped curve. Hope that helped.

suyash1989

As far as the calculation, I can't tell you. But intuitively that problem is easy to figure out. If you expect an investment to earn 10% and it has a 5% std deviation, what is the probability that you'll earn at least 5% in a given year?

It has to be greater than 50% because expected return - Std Deviation is equal to the threshold rate of 5%. So you can eliminate 34% right off the bat. Then you're choosing between 84% and 98%, which is also easy because 98% is obviously not the right answer. That's a fairly large std deviation with the expected return not too far greater than the threshold. Therefore you're left with 84% as the only possible answer.

smartpants

Damil4real, I think we are expected to know that:

+/- 1 std dev = 68%
+/- 2 std dev = 95%
+/- 3 std dev = 99%

Of course, like Conquistador07 said, you can always look it up, but that would cost you time. So, it's in your best interest to know those 3 facts by heart.