The mean per capita income is 24,787 dollars per annum with a variance of 169,744.what is the probability that the sample mean would differ from the true mean by greater than 42 dollars if a sample of 412 persons is randomly selected? round your answer to four decimal places.

0.0385

Step-by-step explanation:

Given : Mean :

Variance :

Standard deviation :  

Sample size :

To find the probability that the sample mean would differ from the true mean by greater than 42 dollars i.e. less than 24,745 dollars and more than 24,829 dollars.

The formula for z-score :-

For x = 24,745 dollars

For x = 24,829 dollars

The P-value=

Hence, the required probability = 0.0385

step-by-step explanation:

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