Question

Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process.

Answer 1

Mean = 0.17

Variance = 0.0068

Explanation:

It is given in the question that the data is uniformly distributed, therefore the mean will be calculated using the formula

Mean =
`(a+b)/(2)`

here, a is the minimum value and b is the maximum value

for the data: 0.15, 0.16, 0.17, 0.18, and 0.19

a = 0.15

b = 0.19

Therefore,

Mean =
`(0.15+0.19)/(2)`

or

Mean =
`(0.34)/(2)`

or

Mean = 0.17

Variance =
`((b-a+1)^2-1)/(12)`

or

Variance =
`((0.19-0.15+1)^2-1)/(12)`

or

Variance = 0.0068