Respuesta :
Answer:
If the warranty limits are at 41.12 months, only 10 percent of the HDTVs need repairs at the manufacturer's expense.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. This means that [tex]\mu = 36.84, \sigma = 3.34[/tex].
Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer's expense?
This is the value of X when Z has a pvalue of 0.90.
Looking at the z-table, we get that this is between [tex]Z = 1.28[/tex] and [tex]Z = 1.29[/tex], so we use [tex]Z = 1.285[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 36.84}{3.34}[/tex]
[tex]X - 36.84 = 1.28*3.34[/tex]
[tex]X = 41.12[/tex]
If the warranty limits are at 41.12 months, only 10 percent of the HDTVs need repairs at the manufacturer's expense.
