Extruded Plastic Rods Are Automatically Cut
The extruded plastic bar is automatically cut to a modest length of 6 inches. What is the actual length ...? 3
Usually divided by an average of 6 inches and a standard deviation of 0.06 inches.
(a) What is the proportion of rods longer than the tolerance limit of 5.9 "to 6.1"?
(b) If 99% of the rods are within tolerance, which standard deviation should be minimized?
1. Use a common distribution: Find the Z score and probability in the table.
z score = (average) / default
z = (x ¼) /
z = (5.96) / 0.06 = 1.6667
Depending on your table, you can find three answers:
zà ƒ = 0.047790352
+ zà = 0.952209648
± zà = 0.904419295
This means that the lower tail (like the upper tail) is 4.77%, the average is 90.44.
%
2. Use the inverse probability of the table:
z = 2.326347874Ã
Working backwards,
z = (x ¼) /
2.326347874Ã = (6.1 6)
= 0.042985832 inches.
