Question

Your company makes ropes used for camping and scouting. The ropes are sold as part of tent kits and individually for the scouts to learn how to tie knots. The manufacturing process is supposed to create ropes 84cms long. As the process is not always accurate, the acceptable range for the ropes length is 83.75cms to 84.2cms. Each hour 30 ropes are randomly selected as they come off the line and measured.

What is the covariance and what numbers do you use to find it?

83.77	84.05	83.88	83.94	84.01	84.03	84.06	84.07	84.09	84.11
84.01	84.09	83.98	83.95	83.92	83.85	83.82	83.83	83.87	83.88
83.91	83.99	84.05	84.07	84.06	84.02	84.01	83.98	83.97	84.01
Mean	83.98	Median	84	Mode	84.01	Std Dev	0.090881	Covariance

Answer 1

The quality characteristics we are interested is based upon the single characteristics.

Let's consider X be the length of the ropes.

Therefore in case of single random variable we calculated Variance.

Also we have,

$Cov(X,X)=Var(X)$

Therefore,

$Var(X)=(Std. Dev)^2$

$Var(X)=(0.090881)^2$

$Var(X)=0.008259356$