Answer:
0.9641 = 96.41% probability that the life span of the monitor will be more than 15,579 hours.
Step-by-step explanation:
Problems of normally distributed samples are 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:
[tex]\mu = 19000, \sigma = 1900[/tex]
Find the probability that the life span of the monitor will be more than 15,579 hours.
This is 1 subtracted by the pvalue of Z when X = 15579. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15579 - 19000}{1900}[/tex]
[tex]Z = -1.80[/tex]
[tex]Z = -1.80[/tex] has a pvalue of 0.0359
1 - 0.0359 = 0.9641
0.9641 = 96.41% probability that the life span of the monitor will be more than 15,579 hours.
