Answer:
Then we can find the probability of interest with this difference:
And using the normal standard distribution or excel we got:
So then the probability that the sample mean would differ from the true mean by less than 28 dollars from the sample of 55 is approximately 0.390
Step-by-step explanation:
We define the variable of interest as the per capita income and we know the following properties for this variable:
and
We want to find this probability:
We select a sample size of n=55 and we define the z score formula given by:
We can find the z score then for 20880 and 20936 and we got:
Then we can find the probability of interest with this difference:
And using the normal standard distribution or excel we got:
So then the probability that the sample mean would differ from the true mean by less than 28 dollars from the sample of 55 is approximately 0.390