7) Your employer, Woodbridge Electric Inc., wants to offer a warranty on the new compact fluorescent light bulb that they have produced and tested. You are called into a meeting and operational experts provide the following data: mean bulb life = 8000 hours, standard deviation = 400 hours (assume a normal distribution). The financial people tell you that the firm cannot afford to replace more than 2.5% of the bulbs under warranty. Some members of the board of directors are pressuring you to come up with a warranty of 7000 hours. The marketing people are pressuring you to create a warranty of 7500 hours. Use the data and adhere to the 2.5% financial constraint above to make your calculations and recommend the highest warranty that you can. What do you recommend as a warranty?

Question

7) Your employer, Woodbridge Electric Inc., wants to offer a warranty on the new compact fluorescent light bulb that they have produced and tested. You are called into a meeting and operational experts provide the following data: mean bulb life = 8000 hours, standard deviation = 400 hours (assume a normal distribution). The financial people tell you that the firm cannot afford to replace more than 2.5% of the bulbs under warranty. Some members of the board of directors are pressuring you to come up with a warranty of 7000 hours. The marketing people are pressuring you to create a warranty of 7500 hours. Use the data and adhere to the 2.5% financial constraint above to make your calculations and recommend the highest warranty that you can. What do you recommend as a warranty?

Answer 1

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.025) and its Z score. Insert into equation above to come to your decision.

Answer 2

To recommend the highest warranty that adheres to the 2.5% financial constraint, we need to determine the warranty that covers the percentage of bulbs that will fail within that time frame.

First, let's calculate the z-score for the desired warranty durations of 7000 hours and 7500 hours. The z-score tells us how many standard deviations a given value is away from the mean.

For a desired warranty of 7000 hours:
z = (x - mean) / standard deviation
z = (7000 - 8000) / 400
z = -2500 / 400
z ≈ -6.25

For a desired warranty of 7500 hours:
z = (x - mean) / standard deviation
z = (7500 - 8000) / 400
z = -500 / 400
z = -1.25

Now, we need to find the corresponding percentage of bulbs failing within the warranty period using the z-table, which provides the area under the standard normal distribution curve.

For a z-score of -6.25, the area to the left of this z-score is practically 0. Therefore, the percentage of bulbs failing within a warranty of 7000 hours is negligible.

For a z-score of -1.25, the area to the left of this z-score is approximately 0.1056. This means that approximately 10.56% of the bulbs will fail within a warranty of 7500 hours.

Since the financial constraint allows for a maximum of 2.5% of bulbs to be replaced, a warranty of 7000 hours is not feasible. However, a warranty of 7500 hours covers approximately 10.56% of the bulbs, which is higher than the financial constraint.

Therefore, the highest warranty that can be recommended is a warranty of 7500 hours.