# statistics

A population forms a normal distribution with a mean of sigma=75 and a standard deviation of 20.

- What proportion of the sample means for samples of n=25 have vales less than 80? In other words, find p(M>79) for n=25

- What proportion of the sample means for n=100 have values greater than 79? In other words, find p(m>79) for n=100.

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1. mean of sample means same as population mean. I assume you have a typo and mean mu = 75

sample s = s/sqrt(n)
if n = 25, then sample sigma = 20/5 = 4

Our 79 is 4 more than the means which is 4/4 = 1.0 sigma above the mean

I assume you have a normal distribution table that says that for various values of z, F(z) = integral from - infinity to z of p(z)
for z = 1 F(z) = .8413. That is the probability of mean of sample being less than 1 sigma greater than mean of population

I think you can repeat that for n = 100. However now they are asking for how many are MORE than 4 from the mean. find the table integral from - infinity to your new z and your answer is 1 - F(z)

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