Question

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.
Approximately how many pixels have a gray scale of between 110 and 140?

A. 30
B. 500,000
C. 680,000
D. 950,000

Answer 1

Let X be a random variable representing the mean gray scale of each pixel.
P(110 ≤ X ≤ 140) = P(X < 140) - P(X < 110) = P(z < (140 - 125)/15) - P(z < (110 - 125)/15) = P(z < 1) - P(z < -1) = P(z < 1) - [1 - P(z < 1)] = 2P(z < 1) - 1 = 2(0.84134) - 1 = 1.68268 - 1 = 0.68268

Number of pixels that have gray scale of between 110 and 140 = 0.68268 x 1000000 = 682680 = approximately 680,000