Suppose that the output of a bottle filling process is normally distributed with a natural process variability of σ = 0.10. The process center has been fixed at 10 ounces. The Upper Spec Limit = 10.2 ounces and the Lower Spec Limit = 9.8 ounces. The liquid costs $0.25 per ounce and the bottles cost $0.50 to fix if they are out of spec. What is the average cost per bottle (filling and fixing) of this process? a. $2.9886 b. $2.5114 c. $2.50 d. $2.5228

d. $2.5228

Step-by-step explanation:

Calculation for the average cost per bottle

As Given,

σ=0.10

μ=10

USL=10.2 oz

LSL=9.8 oz

Liquid cost = $ 0.25 per oz

Bottle cost = $ 0.50 per bottle

First step is to calculate z for USL (Upper Spec Limit)

z for USL = (10.2-10)/0.10 = 2

P(z) = NORMSDIST(2) = 0.9772

Second Step is to calculate z for LSL (Lower Spec Limit)

z for LSL = (9.8-10)/0.1 = -2

P(z) = NORMSDIST(-2) = 0.0228

Third step is to calculate the Proportion out of specifications

Proportion out of specifications = (1-0.9772)+0.0228

Proportion out of specifications= 0.0455

Last step is to calculate the Average cost per bottle (filling and fixing)

Average cost per bottle (filling and fixing) = 10*0.25 + 0.0455*0.5

Average cost per bottle (filling and fixing) =2.5+0.02275

Average cost per bottle (filling and fixing) = $ 2.5228

Therefore the Average cost per bottle (filling and fixing) will be $ 2.5228