Answer:
The expected repair cost is $3.73.
Step-by-step explanation:
The random variable <em>X</em> is defined as the number of defectives among the 4 items sold.
The probability of a large lot of items containing defectives is, <em>p</em> = 0.09.
An item is defective irrespective of the others.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 9 and <em>p</em> = 0.09.
The repair cost of the item is given by:

Compute the expected cost of repair as follows:


Compute the expected value of <em>X</em> as follows:


The expected value of <em>X</em> is 0.36.
Compute the variance of <em>X</em> as follows:


The variance of <em>X</em> is 0.3276.
The variance can also be computed using the formula:

Then the formula of
is:

Compute the value of
as follows:


The expected repair cost is:


Thus, the expected repair cost is $3.73.