Respuesta :
Answer:
The 99.5% confidence interval for the mean battery life is between 119 and 131 hours.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9995}{2} = 0.0025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.0025 = 0.9975[/tex], so [tex]z = 2.81[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.81*\frac{20}{\sqrt{100}} = 6[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 125 - 6 = 119 hours
The upper end of the interval is the sample mean added to M. So it is 125 + 6 = 131 hours.
The 99.5% confidence interval for the mean battery life is between 119 and 131 hours.
