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Question 913:



No answer provided yet.For this question we must assume that the population data we are given are from a normal distribution.

We can use the properties of the normal curve to estimate how likely values are given the mean and standard deviation.  The technique uses something called z-scores, which are just the number of standard deviations a value is from the mean.

Because we're dealing with a sample, we need to compute the standard error of the mean given a sample size of 40.

The standard error (SE)  is calculated as the standard deviation divided by the square root of the sample size: 40/SQRT(49) = 5.714

Now we find out how many standard errors there are between each value 103 and 121 and the population mean of 112. We just subtract the mean from each value and divide that result by the standard error:

(103-112)/5.714 = -1.575
(120-112)/5.714 = 1.575

Next we find the amount of area under the normal curve up to 1.575 using a normal table or the excel function = NORMSDIST(). We get .9423.  We do the same for the smaller z-score and get .0576.

Finally we subtract the smaller area from the larger to get the probability in between = .9423-.0576 = .887.
So the probability a sample mean from a sample size of 49 falls between those two points is .885.

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