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# Probability

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30) An image is partitioned into 2 regions - one white and the other black. A reading taken from a randomly chosen point in the white section will give a reading that is normally distributed with Mean=4 and Variance =4, whereas one taken from a randomly chosen point in the black region will have a normally distributed reading with parameters (6,9). A point is randomly chosen on the image and has a reading of 5. If the fraction of the image that is black is alpha, for what vlaue of alpha would the probability of making an error be the same whether one concluded the point was in the black region or in the white region?

NOTE: Black is N(6, 3) (9 = variance)

https://brainmass.com/math/probability/probability-36659

#### Solution Preview

Black is N(6, 3) (9 = s^2)
White is N(4, 2) (4 = s^2)

White
Mean=M = 4.00
Standard deviation =s= 2.00
x= 5.00
z=(x-M )/s 0.5 =(5-4)/2
Cumulative Probability corresponding to z= 0.5 is= 0.6915
Therefore probability corresponding to x> 5.00 is 1-Prob(Z)= 0.3085 =1-0.6915
0r= 30.85%
Probability= 30.85%

Probability of finding a value greater than or ...