The lengths of plate glass parts are measured to the nearest tenth of a millimeter. The lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.8. Determine the mean of the lengths.

590.45

0.0825 mm^2

Step-by-step explanation:

Let us introduce the discrete uniform random variable Y with the parameters:

a = 0, b = 9

Calculate the mean and the variance:

E (Y) = 0 + 9 / 2 = 4.5

Var (Y) = (9-0+1) ^2-1/12=8.25

Now observe that the random variable in the exercise - denoted X - is in fact:

X = 590 + Y/10

Now calculate:

E (X) = E (590.1 + Y/10) = 590.1 + E (Y) / 10=590.45

Var (X) = E ((X - E (X)) ^2) = E ((590 + Y/10-590 - E (Y) ^2/10)

=E ((Y - E (Y)) ^2) / 10

= Var (X) / 100

= 0.0825 mm^2