A company estimates that 0.2% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $450.

If they offer a 2 year extended warranty for $55, what is the company's expected value of each warranty sold?

IT'S 54.1

ev=55-.002*450=55-.90 check my math

To calculate the company's expected value of each warranty sold, we need to consider the probability of a product failing without an extended warranty and the replacement cost.

Step 1: Calculate the probability of a product failing after the original warranty period but within 2 years of purchase.
The company estimates that 0.2% of their products will fail within this time frame. Convert this to decimal form: 0.2% = 0.002.

Step 2: Calculate the expected replacement cost.
The replacement cost for a failed product is $450.

Step 3: Determine the total expected cost of a product failing without an extended warranty.
Multiply the probability of failure by the replacement cost: 0.002 * $450 = $0.90.

Step 4: Calculate the expected value of each warranty sold.
Subtract the cost of the warranty ($55) from the expected cost of a product failing without a warranty. This represents the savings from having an extended warranty: $0.90 - $55 = -$54.10.

The company's expected value of each warranty sold is -$54.10.

To find the company's expected value of each warranty sold, we need to calculate the probability of a product failing after the original warranty period but within 2 years of purchase and the associated cost of replacement for that failure.

Let's break down the calculation step by step:

Step 1: Calculate the probability of a product failing after the original warranty period but within 2 years of purchase.
The company estimates that 0.2% of their products will fail within this time frame. We can represent this as a decimal by dividing 0.2 by 100: 0.2/100 = 0.002.

Step 2: Calculate the replacement cost for a failed product.
The replacement cost of a failed product is given as $450.

Step 3: Calculate the expected value of each warranty sold.
To calculate the expected value of each warranty sold, we need to multiply the probability of a product failing (from step 1) by the replacement cost (from step 2) and subtract the cost of the warranty ($55).
Expected Value = (Probability of failure * Replacement cost) - Cost of warranty

Expected Value = (0.002 * $450) - $55

Expected Value = $0.9 - $55

Expected Value = -$54.1

The company's expected value for each warranty sold is -$54.1.

Please note that a negative value means that, on average, the company would expect to lose money for each warranty sold.