Question

Question 12 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 0.98 millimeters. (b) What thickness is exceeded by 90% of the flanges? millimeters (c) Determine the mean and variance of flange thickness. millimeters Mean = millimeters (Round your answer to 6 decimal places.) Variance Statistical Tables and Charts

Answer 1

Answer:

a)

To determine the proportion of flanges that exceed 0.98 millimeters

P(X > 0.98) = (1.05 - 0.98) / (1.05 - 0.95)

= 0.07 / 0.1

Proportion of flanges that exceeds 0.95 millimeters = 0.7

b)

To give thickness by 90%of flanges

P(X > x) = 0.9 or

(1.05 - x) / (1.05 - 0.95) = 0.9

(1.05 - x) / 0.1 = 0.9

1.05 - x = 0.9 * 0.1

x = 1.05 - 0.9 * 0.1

x = 1.05 - 0.09

Thickness = x = 0.96 millimeters

c)

To determine the mean & variance of flange thickness

Mean = (0.95 + 1.05) / 2

= 2/2

= 1

Mean = 1 millimeter

Variance = (1.05 - 0.95)^2 / 12

= 0.1^2 / 12

= 0.01/12

= 0.000833

Variance = 0.000833 millimeters