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| Math Central | Quandaries & Queries |
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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? |
Candace,
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?
Harley
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