Statistics for Decision- Making in Business - Maricopa Community ...

An expected value is actually not something terribly new. To see this more explicitly,
suppose a student earns three test scores: 95%, 80%, and 85%. Then the average
percentage is:
Observe that we can use properties of fractions to separate the sum as follows:
( ) ( ) ( )
While one-third in this situation is not a probability (since the scores have already been
) “ ” -third of the overall
class grade.
Example 1:
A company sells consumer electronics, such as televisions, stereos, and
computers. For each product, the company offers the consumer
a warranty that protects any problems that might occur within
the first two years, with the exception of accidental damage
and theft. For a particular television that runs $1200, it offers a
2-year warranty for $ ’
determines that 3% of these televisions malfunction each year.
Is the company offering the warranty at a profitable price
Explain your answer and define the random variable.
SOLUTION: We should determine what will happen, on average. We first see that the
warranty is a 2-year warranty and the defect rate is for one year. If 3% malfunction each
year, then 6% of all televisions are expected to malfunction within the first two years.
This means that the company will make $175 with a 94% probability and will lose $1200-
$175=$1025 with a 6% probability, since it will still receive the payment, but will have to
either replace the product or offer a credit to the consumer.
Letting
, -, is
, then the expected amount to be gained, or
, - ( )
Statistics for Decision-Making in Business © Milos Podmanik Page 137