**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 Â¼) /

z = (5.96) / 0.06 = 1.6667

Depending on your table, you can find three answers:

zÃ ƒ = 0.047790352

+ zÃ = 0.952209648

± zÃƒ = 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 Â¼) /

2.326347874Ã = (6.1 6)

= 0.042985832 inches.