Chapter 10.4, Problem 12E

Solution

To determine: The expected values and explain that you should purchase the extended coverage or not.

We are expected to make a loss of $29 when purchasing the extended coverage, which implies that we should not purchase the extended coverage.

Given information:

5% of the customers require a $300 for repair, and the extended warranty costs is $49.

1% of the customers require a $500 for repair, and the extended warranty costs is $49

Formula used:

For calculating the expected value or mean use the following formula,

  $\mu ={\displaystyle \sum xP\left(x\right)}$   ...... (1)

Calculation:

5% of the customers require a $300 repair, while the extended warranty costs $49 and thus a profit of $300-$49=$251, Then find:

  $\begin{array}{c}P\left(\$251\right)=5\%\\ =0.05\end{array}$

1% of the customers require a $500 repair, while the extended warranty costs $49 and thus a profit of $500-$49=$451, Then find:

  $\begin{array}{c}P\left(\$451\right)=1\%\\ =0.01\end{array}$

The remaining 100%-5%-1% = 94% of the customers do not repair, while the extended warranty cost $49 and thus a loss of $49,Then find:

  $\begin{array}{c}P\left(-\$49\right)=94\%\\ =0.94\end{array}$

The expected value (or mean value) is the sum of the product of each possibility x with its probability P(x).

  $\begin{array}{c}\mu ={\displaystyle \sum xP\left(x\right)}\\ =\$251\times 0.05+\$451\times 0.01+\left(-\$49\right)\times 0.94\\ =-\$29\end{array}$

Thus, we are expected to make a loss of $29 when purchasing the extended coverage, which implies that we should not purchase the extended coverage.