Question

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A gray-scale digital camera with 1,000,000 pixels takes a picture (the picture is made of 1,000,000 parts and each part has a certain amount of gray). A histogram is made where the data is the amount of gray in each of these parts. The histogram looks bell-shaped with a mean of 125 gray levels and a standard deviation of 15.

How many pixels are brighter than 163 gray levels?

5000
10,000
160,000
50,000

Answer 1

5000
First, let's determine how many standard deviations from the mean the value
(163+1) = 164 is:
(164 - 125)/15 = 39/15 = 2.6
Now using a standard normal table, look up 2.6 to determine the percentage of points that would be that far from the mean. I find a value of 0.49534. Note that is is a half value. So the percentage that will be higher than that will be 0.5 - 0.49534= 0.00466
Now multiply by the number of points overall, getting
0.00466 * 1000000 = 4660
So there will be approximately 5000 pixels brighter than 163 gray levels.