Respuesta :
Answer:
The 96% confidence interval for the population mean of all bulbs produced by this firm is between 765 hours and 795 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{1-0.96}{2} = 0.02[/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 1-0.02 = 0.98, so z = 2.055
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.
So
[tex]M = 2.055*\frac{40}{\sqrt{30}} = 15[/tex]
The lower end of the interval is the mean subtracted by M. So 780 - 15 = 765 hours.
The upper end of the interval is M added to the mean. So 780 + 15 = 795 hours.
The 96% confidence interval for the population mean of all bulbs produced by this firm is between 765 hours and 795 hours.
