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

answer: d. $20

step-by-step explanation:

just took the test

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be