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danksans4912
24.07.2019 •
Mathematics
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.
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Ответ:
0.5467
Step-by-step explanation:
Let X be the random variable that represents the income (in dollars) of a randomly selected person.
Given :![\mu=15451](/tpl/images/0128/1826/0a99d.png)
Sample size : n=350
z-score :![\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}](/tpl/images/0128/1826/80155.png)
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.
Ответ: