Question

Cook-Easy deep fryer has a mean time before failure of 39 months with a standard deviation of 4 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the deep fryers returned?

Answer 1

The warranty period for the Cook-Easy deep fryer should be 34 months to ensure that the manufacturer will not have more than 8% of the deep fryers returned.

Step-by-step explanation:

To calculate the warranty period for the Cook-Easy deep fryer, we need to find the length of time that corresponds to the 8th percentile of the failure times. Since the failure times are normally distributed with a mean of 39 months and a standard deviation of 4 months, we can use the Z-score formula to find the corresponding value.

Z = (X - μ) / σ

where Z is the Z-score, X is the value we want to find, μ is the mean, and σ is the standard deviation. Rearranging the formula, we have X = Z * σ + μ.

Since we want the 8th percentile, which corresponds to a Z-score of -1.405, we can plug in the values to find the warranty period:

X = -1.405 * 4 + 39 = 33.58 months.

Therefore, the warranty period should be rounded up to 34 months to ensure that the manufacturer will not have more than 8% of the deep fryers returned.