Question

Cook-easy rice cooker has a mean time before failure of 35 months with a standard deviation of 5 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 10% of the rice cookers returned? round your answer down to the nearest whole number.

Answer 1

The warranty period should be rounded down to 28 months.

Step-by-step explanation:

To calculate the warranty period, we need to find the length of time that corresponds to the upper 10% of the distribution. Since the failure times are normally distributed with a mean of 35 months and a standard deviation of 5 months, we can use the z-score formula to find the z-score corresponding to the 10th percentile.

z = (x - μ) / σ

Using a z-table or calculator, we can find that the z-score corresponding to the 10th percentile is approximately -1.28. Now, we can solve for x:

-1.28 = (x - 35) / 5

x - 35 = -1.28 * 5

x - 35 = -6.4

x = 35 - 6.4

x = 28.6

Therefore, the warranty period should be rounded down to 28 months.