Question 1185302: we want to estimate the mean of a population a random sample of subjects is selected and the sample mean is competed what is the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i get the following:
if the sample mean is within 3 units of the population mean and the standard error is 1.8, then:
the lower z-score is equal -3/1.8 = -1.6666667 and the higher z-score is equal to 3/1.8 = 1.66666667.
the area under the normal distribution curve between these two z-score values is .9044193393.
that is the probability that the true population mean will be within 3 units of the sample mean.
as an example of what i think is the answer, assume any sample mean, such as 5342.
if the real population mean can be as much as 3 units below this, then the lower x-score is 5339.
if the real population mean can be as much as 3 units above this, then the upper x-score is 5345.
to find the lower and higher z-scores, use the z-score formula to get:
lower z = (5339 - 5342) / 1.8 = -3/1.8 = -1.66666667.
higher z = (5345 - 5342) / 1.8 = 3/1.8 = 1.66666667.
the area between these two z-scores is the same as shown above.
that is equal to .9044193393.
based on these figures, the sample mean can be anything, as long as the standard error is 1.8 and the lower and higher figures are 3 units below and above that mean.
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