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
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
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