Question

Suppose I choose to model a symmetrical distribution with the normal distribution without deleting values below a given minimum and above a given maximum. I also model it with a beta distribution, using alpha- beta -3. If the minimum is 10, the maximum 20, the average 15, the standard deviation of the normal is 2.3, what is the absolute difference in the probability of a value being larger than 17 when comparing the normal to the beta simulation?

Answer 1

Here first calculation the probability of a value being larger than 17 with normal distribution.

Pr(x > 17; 15 ; 2.3) = 1 - Pr(x < 17 ; 15 ; 2.3)

Z = (17 - 15)/2.3 = 0.8696

Pr(x > 17; 15 ; 2.3) = 1 - Pr(x < 17 ; 15 ; 2.3) = 1 - Pr(Z < 0.8686) = 1 - 0.8075 = 0.1925

Now with beta distribution where alpha and beta equals to 3.

Pr(x > 17 ; 3; 3) = 1 - BETADIST (x < 17 ; 3 ; 3 ; 10 ; 20)

= 1 - 0.8369 = 0.1631

Absolute differene in the probabilities are = 0.1925- 0.1631 = 0.0295