Math

QuestionA company estimates 0.5%0.5\% product failure post-warranty, costing \150.Ifa2yearwarrantyis$19,findprofit150. If a 2-year warranty is \$19, find profit x$ values and expected value.

Studdy Solution

STEP 1

Assumptions1. The failure rate of the products after the original warranty but within years is0.5% . The replacement cost for each failed product is 1503.Thecompanyoffersayearextendedwarrantyfor1503. The company offers a-year extended warranty for 194. The profit (x) could be negative in case of a loss5. The probability distribution table needs to be completed from the company's point of view

STEP 2

First, we need to identify the possible outcomes for the company. There are two possible outcomes1. The product fails and the company has to pay the replacement cost. This happens with a probability of0.5%.
2. The product does not fail and the company keeps the warranty fee. This happens with a probability of99.5% (100% -0.5%).

STEP 3

Now, we calculate the profit for each outcome.1. If the product fails, the company's profit is the warranty fee minus the replacement cost.
2. If the product does not fail, the company's profit is the warranty fee.

STEP 4

Plug in the given values to calculate the profit for each outcome.
1. If the product fails, the profit is 1919 - 150 = -131.<br/>2.Iftheproductdoesnotfail,theprofitis131.<br />2. If the product does not fail, the profit is 19.

STEP 5

Now, we can complete the probability distribution table.\begin{array}{|c|c|} \hlinex &(x) \\ \hline-\$131 &0.005 \\ \$19 &0.995 \\ \hline\end{array}

STEP 6

The expected value is the sum of each outcome multiplied by its probability. We can calculate this using the formula(x)=x(x)(x) = \sum x \cdot(x)

STEP 7

Plug in the values from the probability distribution table to calculate the expected value.
(x)=($131×0.005)+($19×0.995)(x) = (-\$131 \times0.005) + (\$19 \times0.995)

STEP 8

Calculate the expected value.
(x)=$0.655+$18.905=$18.25(x) = -\$0.655 + \$18.905 = \$18.25The company's expected value of each warranty sold is $18.25.

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