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 140a. 30

b. 500,000
c. 680,000
d. 950,000

Answer 1

c. 680,000

Explanation:

Because the histogram looks bell-shaped, the distribution can be assumed to be normal.

The mean, μ, is 125 and the standard deviation, σ, is 15.

The empirical rule of normal distribution is 68-95-99.7. This rule means that 68% of the distribution lies within μ - σ and μ + σ, 95% lies within μ - 2σ and μ + 2σ and 99.7% lies within μ - 3σ and μ + 3σ.

Between 110 and 140, we have

110 = 125 - 1(15)

140 = 125 + 1(15)

Hence, this range is μ - σ and μ + σ. The percentage is 68%.

68% × 1,000,000 = 680,000