Q:
XYZ Company stocks have an expected return of 12% and a standard deviation of 8%. Assuming that the returns of this company are a continuous random variable that is normally distributed, what is the probability that the returns will be -1.2% or less?
A) 45%
B) 1.65%
C) 10%
D) 5%
A:

First, transform the actual value of this outcome (-1.2%) into its standardized z-score:
Zx= [(X - ux) ÷ σx] = [(-1.2 - 12.0) ÷ 8] = -1.65
Using the Normal Rule, candidates should realize that approximately 90% of the outcomes are expected to occur within 1.65 standard deviations of the mean. This would mean that 45% (half of 90%) of the observations must lie within the mean and -1.65 standard deviations away from the mean. If this is so, then 5% of all the observations must lie below -1.65 standard deviations away from the mean.

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