Answer:
The confidence interval will be given by:
, in which z is related to the confidence level.
For a confidence level of x%, z is the value in the z-table that has a pvalue of ![1 - \frac{1 - z}{2}](https://tex.z-dn.net/?f=1%20-%20%5Cfrac%7B1%20-%20z%7D%7B2%7D)
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In the context of this problems:
It means that the sampling distributions of the sample mean of 500 components will be approximated normal, with mean 200,000 and standard deviation ![s = \frac{1000}{\sqrt{500}} = 44.72](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B1000%7D%7B%5Csqrt%7B500%7D%7D%20%3D%2044.72)
To build the confidence interval:
The confidence interval for the average length of life of the electronic components they produced will be given by:
, in which z is related to the confidence level.
For a confidence level of x%, z is the value in the z-table that has a pvalue of ![1 - \frac{1 - z}{2}](https://tex.z-dn.net/?f=1%20-%20%5Cfrac%7B1%20-%20z%7D%7B2%7D)