Question

Eco-Cook juicer has a mean time before failure of 35 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 juicers returned?

Answer 1

The warranty period should be rounded up to 29 months.

Step-by-step explanation:

To find the warranty period so that the manufacturer will not have more than 8% of the juicers returned, we need to find the z-score corresponding to the 8th percentile. The formula to calculate the z-score is: z = (x - mean) / standard deviation. Plugging in the appropriate values, we have z = (x - 35) / 4. Using a z-table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.405. Now we can solve for x: -1.405 = (x - 35) / 4. Rearranging the equation, we get x = -1.405 * 4 + 35 = 28.58. Therefore, the warranty period should be rounded up to 29 months.