Distribution and Std Deviation

[[email protected]]

Hi David,

2006 past year question
Question:
Let X be a uniformly distributed random variable between minus one and one so that the standard deviation of X is 0.577. What percentage of the distributions will be less than 1.96 std deviations above the mean?
A: 100%
B: 97.5%
C: 95%
D: Insufficient information provided.


Answer: A 100%
The answer requires understanding of distributions and std deviation. The key is that every distribution has a std distribution. However the number of std deviations associated with different probabilities are different for each distribution. In this case 1.96 std deviation represents a move of 1.12 or less. As the total distribution is defined as falling between minus one and one.

Can you explain how to solve this question? I do not have a clue of what the question is asking even after reading the answer.

Your guidance, please

Regards
Learning.

 

[David Harper CFA FRM]

Hi Learning, it's a pretty lame question. The uniform distribution is bounded here from -1.0 to +1.0; 1.96 standard deviations is 1.96*0.577 = +1.13 or 1.12 above the mean of zero, which is "all the way over to the right" beyond the +1.0, so the entire distribution (100%) is to the left - David