Respuesta :
Answer:
0.0918 = 9.18% probability that the battery life is at least 8.1 hours.
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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean 7.5 hours
This means that [tex]\mu = 7.5[/tex]
Standard deviation 27 minutes.
An hour has 60 minutes, which means that [tex]\sigma = \frac{27}{60} = 0.45[/tex]
What is the probability that the battery life is at least 8.1 hours?
This is 1 subtracted by the p-value of Z when X = 8.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.1 - 7.5}{0.45}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a p-value of 0.9082.
1 - 0.9082 = 0.0918
0.0918 = 9.18% probability that the battery life is at least 8.1 hours.
