Mean and Variance

Question

The lengths of plate glass parts are measured to the nearest tenth or a millimeter. The lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.0 and continuing through 590.7. Determine the mean and variance of the lengths rounded 3 decimal places.

Answer 1

In a discrete uniform distribution, you can calculate the mean using the formula:

Mean = (a + b) / 2

Here, a=590.0a=590.0 and b=590.7b=590.7, so the mean would be:

Mean = (590.0 + 590.7) / 2 = 1180.7 / 2 = 590.35

The variance can be calculated using the formula:

Variance = ((b - a + 0.1)^2 - 0.01) / 12

For a=590.0a=590.0 and b=590.7b=590.7, the variance would be:

Variance = ((590.7 - 590.0 + 0.1)^2 - 0.01) / 12 = ((0.7 + 0.1)^2 - 0.01) / 12 = (0.8^2 - 0.01) / 12 = (0.64 - 0.01) / 12 = 0.63 / 12 = 0.0525

So, the mean length of the plate glass parts is 590.35 mm, and the variance is 0.053, rounded to 3 decimal places as requested.