Math CentralQuandaries & Queries


Question from Candace, a student:

If a normal-shaped distribution has a mean of 80 and a standard deviation of 15 what is the z-score for M=84 for a sample of n=25 scores. Is this sample mean in the middle 95% of the distribution?


Use my response to Crystal to find the mean (μm) and standard deviation (σm) of the distribution of sample means of samples of size n = 25. Convert the value of M = 84 to its z-value using

z = (M - μm)/σm

Using the standard normal table you can see that Pr(-1.96 < z < 1.96) = 0.95. Is the z-value you found between -1.96 and 1.96?


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