CFA® Level 1: Coefficient of Variation Calculation

Coefficient of Variation for a Normally Distributed Variable

Prev Question Next Question

Question

Variable X is distributed normally and has a mean of 10. If the probability that an observation of X will be negative is 0.16, what is the coefficient of variation of X?

Answers

Explanations

Click on the arrows to vote for the correct answer

A. B. C. D.

B

The probability that X lies a distance 10 below the mean is given to be 0.16. Since the normal distribution is symmetric about the mean, this implies that the probability that X will be 10 greater than the mean is also 0.16. Thus, the probability that X lies between 0 and 20 is 1-0.16-0.16 = 0.68. For a normal distribution,

68% of the observations lie within one standard deviation of the mean. Hence, the standard deviation of X equals 10. The coefficient of variation is then equal to standard deviation/mean = 10/10 = 1.

Prev Question Next Question