can you help me find the solution to this? what is the answer? Please show calcu

Question

can you help me find the solution to this? what is the answer? Please show calculations

Problem No.4 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

Explanation / Answer

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

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