Z of +1.00 indicates that an EPS of $8 is one standard deviation above the mean, and a Z of -2.00 shows that the EPS of $2 is two standard deviations below the mean. Using the symmetric properties of the normal distribution, we can approximate that the probability of the EPS falling between $2 and $8 is 0.475 + 0.34 = 0.815.
o: Calculate probabilities using the standard normal probability distribution.
With the aid of a normal probability table, we can precisely compute the probability of a normally distributed random variable falling between any two values.
Example:The Z table tells us that F(2) = 0.9772, thus F(-2) = 1 - .09772 = 0.0228. This tells us that 0.0228 or 2.28% of the area falls below Z = -2 and an equal amount falls above Z = +2. Furthermore, P(-2 ≤ Z ≤ 2) = 1 - 0.0228 - 0.0228 = 0.9544.Another way to do this is to write:
P(-2 ≤ Z ≤ 2) = F(2) - F(2) = 0.9772 - 0.0228 =0.9544.
p: Distinguish between a univariate and a multivariate distribution.
A multivariate distribution specifies the probabilities for a group of random variables. It is meaningful when the random variable in the group are not independent. A joint probability table describes the multivariate distribution between two discrete random variables. Multivariate relationships can exist between two or more continuous random variables, e.g., inflation, unemployment, interest rates, and exchange rates.
A multivariate normal distribution applies when all the random variables have a normal distribution. As mentioned earlier, one of the characteristics o