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 .

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

boxplot e is the answer