Respuesta :
Answer:
She should offer a guarantee of 13.76 years.
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 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.
The average life of a certain type of small motor is 10 years with a standard deviation of 2 years.
This means that [tex]\mu = 10, \sigma = 2[/tex]
If she is willing to replace 3% of the motors that fail, how long a guarantee (in years) should she offer?
She should offer the 100 - 3 = 97th percentile as a guarantee, so X when Z has a pvalue of 0.97, that is, X when Z = 1.88.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.88 = \frac{X - 10}{2}[/tex]
[tex]X - 10 = 2*1.88[/tex]
[tex]X = 13.76[/tex]
She should offer a guarantee of 13.76 years.
