The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the proportion of flanges that exceeds 0.99 millimeters.

The proportion of flanges that exceeds 0.99 millimeters is 0.6

Explanation:

Given;

integral range of [0.95,  1.05]

Let X be a variable with uniform distribution over the given range.

1 - 0.95 = 0.05, 1.05 - 1 = 0.05

interval = 10 - 0.5 = 9.5

F(x) = 10x + 9.5

When, X exceeds 0.99 millimeters, then the proportion of flanges will be;

P (X > x) = 1 - F(x)

P( X > 0.99 ) = 1 - 10(0.99) + 9.5

P( X > 0.99 ) = 0.6

Therefore, the proportion of flanges that exceeds 0.99 millimeters is 0.6