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
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
![\alpha = \frac{1-0.96}{2} = 0.02](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B1-0.96%7D%7B2%7D%20%3D%200.02)
Now, we have to find z in the Ztable as such z has a pvalue of ![1-\alpha](https://tex.z-dn.net/?f=1-%5Calpha)
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
![M = z*\frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%2A%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
In which
is the standard deviation of the population and n is the size of the sample.
So
![M = 2.055*\frac{40}{\sqrt{30}} = 15](https://tex.z-dn.net/?f=M%20%3D%202.055%2A%5Cfrac%7B40%7D%7B%5Csqrt%7B30%7D%7D%20%3D%2015)
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.