A company estimates that 0.7% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $300.

If they offer a 2 year extended warranty for $47, what is the company's expected value of each warranty sold?

Question

contestada

Respuesta :

pedrocarratore pedrocarratore · Answer 1 · 2019-12-13T05:01:01+01:00

Answer:

$44.90

Step-by-step explanation:

The resulting value for the company of replacing a failed product is given by the price of the warranty minus the cost of replacement:

[tex]F= \$47-\$300 =-\$253[/tex]

This event has a 0.7% chance of happening.

The resulting value for selling extended warranty to a product that does not fail is given by the proce of the warranty:

[tex]W= \$47[/tex]

This event has a 99.3% chance of happening.

The expected value is:

[tex]EV = \$47*0.993+(\$47-\$300)*0.007\\EV=\$44.90[/tex]

The expected value for each warranty sold is $44.90.

joaobezerra joaobezerra · Answer 2 · 2022-03-03T12:06:56+01:00

Using the discrete distribution, it is found that the company's expected value of each warranty sold is of $44.9.

The mean is given by the sum of each outcome multiplied by it's probability.

The standard deviation is given by square root of the sum of the difference squared of each outcome and the mean, multiplied by it's respective probability.

In this problem, considering the scenario described, we have that the distribution is:

P(X = -253) = 0.007 -> 253 as the company gets the warranty of $47 but has to pay $300, 300 - 47 = 253

P(X = 47) = 0.993

Hence the expected value is:

E(X) = -253(0.007) + 47(0.993) = 44.9.

The company's expected value of each warranty sold is of $44.9.

More can be learned about the mean and the standard deviation of a discrete distribution at https://brainly.com/question/24855677