Respuesta :
Answer:
The 12th percentile of the working lifetime is 7.65 years.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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 question, we have that:
[tex]\mu = 10, \sigma = \sqrt{4} = 2[/tex]
12th percentile:
X when Z has a pvalue of 0.12. So X when Z = -1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.175 = \frac{X - 10}{2}[/tex]
[tex]X - 10 = -1.175*2[/tex]
[tex]X = 7.65[/tex]
The 12th percentile of the working lifetime is 7.65 years.
