Question
In: Statistics and Probability
The mean capita income is 15,451 dollars per annum with a variance of 298,116. What Is...
The mean 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 greater than 22 dollars if a sample of 350 persons is randomly selected? Round answer to dour decimal places.
Solutions
Expert Solution
Solution :
Given that,
mean = 
= 15451
variance = 
2= 298116
standard deviation =
= 546
n = 350
=
= 15451
=
/ 
n = 546 /
350 = 29.1849
P( 15429 < 
< 15473) = P((15429 - 15451) /29.1849 <(
-
)
/
< (15473 - 15451) / 29.1849))
= P(-0.75 < Z < 0.75)
= P(Z < 0.75) - P(Z < -0.75) Using z table,
= 0.7734 - 0.2266
= 0.5468
Probability = 0.5468
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