CFA Practice Question

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CFA Practice Question

Suppose a set of data has a mean of 52 and a standard deviation of 6. According to Chebyshev's Theorem, at least what percentage of the data lies between 40 and 64? If the data is normally distributed, about what percentage of the data lies between 40 and 64, according to the Empirical Rule?

A. 0%, 68%
B. 75%, 95%
C. 94%, 100%
Correct Answer: B

User Contributed Comments 11

User Comment
Pooh Chebyshev's inequality formula says: 1-(1/c^2).
First find the standardized normal deviation: 40=52+6x or 40=52-6x; x=2
By chebyshev: 1-(1/2^2) =.75
By Empirical Rule: 95% within 2 s
cwrolfe Notice that none of the answers for the empirical rule are alike and that the range is +/- 2 std. deviations...99.7%.

95% is 1.95 std. dev. Pooh
cwrolfe ...correction...1.96
bobert Chebychev: 75% @ 2s
Empirical: 95% @ 2s
Confidence Interval: 95% @ 1.96s
Raok forgot chebychev formula already...
dhess0 me too
EminYus ya by the time i get to the next chapter, all is forgot...i guess this is what the review is for
johntan1979 Chebyshev = more conservative dispersion estimate

Applies to ANY probability distribution irregardless of the shape of the mound i.e. doesn?t have to be normal
sharky7 @Pooh How have you calculated the standardized normal deviation?
irapp92 @sharky7 Pooh found the standardized normal distribution in a sort of roundabout way..

I would just stick to finding it by using z= (X-u)/stdv

Chebyshev's equation is by rule the very minimum number of observations that lie less than c standard deviations from the mean. It is far more conservative than the assumptions made by the normal distribution model. I think you just have to memorize the empirical rules and the normal distribution rules and remember that they're not the same because they come from different models.
farhan92 i did 1 - 1/(52^2) and realised that was bollocks so just eliminated using the 2sd=95%
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