Question

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.

Answer 1

590.45

0.0825 mm^2

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