Respuesta :
Answer:
The warranty period should be of 30 months.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Eco-Cook rice cooker has a mean time before failure of 38 months with a standard deviation of 6 months.
This means that [tex]\mu = 38, \sigma = 6[/tex]
What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the rice cookers returned?
The warranty period should be the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.405 = \frac{X - 38}{6}[/tex]
[tex]X - 38 = -1.405*6[/tex]
[tex]X = 30[/tex]
The warranty period should be of 30 months.
