Respuesta :
Answer:
86.64% probability that such brakes last between 54,000 and 66,000 miles
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 [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 = 60000, \sigma = 4000[/tex]
What is the probability that such brakes last between 54,000 and 66,000 miles?
This is the pvalue of Z when X = 66000 subtracted by the pvalue of Z when X = 54000.
X = 66000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{66000 - 60000}{4000}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332
X = 54000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{54000 - 60000}{4000}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.9332 - 0.0668 = 0.8664
86.64% probability that such brakes last between 54,000 and 66,000 miles
