Answer:
The mean of the cable length is
The standard deviation of the cable length is
Half of the cables lie in the specifications.
Step-by-step explanation:
<em>Point a:</em>
Suppose <em>X</em> is a continuous random variable with probability density function <em>f(x).</em>
The mean of a continuous random variable, denoted as <em>μ</em> or <em>E(X)</em> is<em> </em>
<em></em>
The standard deviation of <em>X</em> is
where is the variance of X
We know that the probability density function of the length of computer cables is
Applying the above definition of the mean we get
Applying the above definition of the standard deviation we get
First we need to calculate the variance of X
<em>Point b:</em>
To find what proportion of cables is within specifications you need to: