C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of {eq}4 \pm 0.003 {/eq} inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of 0.002 inch.
a. Calculate the {eq}C_{pk} {/eq} for this machine
b. Should C-Spec use this machine to produce this part? Why?

Step-by-step explanation:

Given that :

sample mean = 4.001 inches

sample standard deviation = 0.002 inch

a.

specification =

Upper specification limit USL = 4 + 0.003  = 4.003

Lower specification limit LSL =  4 - 0.003 = 3.997

Thus ;

 = 0.333

 is a measure of closeness to one's target and the consistency around the average performance.

b) No, C - spec should not use this machine to produce this part because <  1.33 which typical means that the part is not fully capable of hitting the target specification on a consistent basis .

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

b

step-by-step explanation: