The thickness of a conductive coating in micrometers has a density function of 500x-2 for 113 μm < x < 146 μm and zero for x elsewhere. (a) determine the mean and (b) variance of the coating thickness. round your answers to one decimal place (e. g. 98.7). (c) if the coating costs 0.60 per micrometer of thickness on each part, what is the average cost of the coating per part? round your answer to two decimal places (e. g. 98.76).

The mean, variance and cost of coating are obtained from the

given density function by integration.

Correct response:

(a) The mean, μ is approximately 128.11 μm

(b) The variance is approximately 87.8

(c) Average cost of coating per part is approximately $76.87

The given density function is; 500·x⁻² for 113 μm < x < 146 μm

(a) The mean value is; μ = E(x)

(b) The variance is given as follows;

Which gives;

Which gives;

(c) The cost of coating per micrometer thickness = $0.60

The average cost of coating per part is therefore;

E(X) = The mean coating thickness × Cost per micrometer thickness

Which gives;

E(0.6) = 0.6 × 128.11 ≈ 76.87

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