Question

Consider that in a Decision Tree, the outcome of one of the chance events is normally distributed with mean 25 and standard deviation 10. You decided to approximate this chance event by utilizing the Extended Pearson-Tukey Method. What would be one of the outcomes of the final chance event that you would associate a probability of 0.185?

The standard normal distribution (N(0,1)) has the following percentile table:

X	0	0.13	0.26	0.39	0.53	0.68	0.84	1.04	1.28	1.65
P(x<=X)	0.5	0.55	0.60	0.65	0.70	0.75	0.80	0.85	0.90	0.95
percent	50	55	60	65	70	75	80	85	90	95

(You can read the table as follows; 65^thpercentile for N(0,1) is 0.39)

Answer 1

What would be one of the outcomes of the final chance event that you would associate a probability of 0.185?

Answer: One of the final outcome of the final chance event we should associate a probability of 0.185 is 41.5.

EXPLANATION:

In case of Extended Pearson-Tukey Method, we assign probabilities of 0.185 with the 0.05 fractle and 0.95 fractile event.

From the percentile table,

the 95th percentile (0.95) has a standard normal value N(0,1) of 1.65.

The corresponding value for N(25,10) = =25+1.65*10 =41.5