The mean per capita income is 15,451 dollars per annum with a variance of 298,116. what is the probability that the sample mean would differ from the true mean by less than 22 dollars if a sample of 350 persons is randomly selected? round your answer to four decimal places.

0.5467

Step-by-step explanation:

Let X be the random variable that represents the income (in dollars) of a randomly selected person.

Given :

Sample size : n=350

z-score :

To find the probability that the sample mean would differ from the true mean by less than 22 dollars, the interval will be

For x=15429

For x=15473

The required probability :-

Hence, the required probability is 0.5467.

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