document.write( "Question 942035: Find the mean and standard error of the sample means that is normally distributed with a mean of 10 and a standard deviation of 2 and a sample size of 25.
\n" ); document.write( "Using the above distribution find the probability of a score less than 11.
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Algebra.Com's Answer #574220 by stanbon(75887)\"\" \"About 
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Find the mean and standard error of the sample means that is normally distributed with a mean of 10 and a standard deviation of 2 and a sample size of 25.
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\n" ); document.write( "Ans:: mean of the sample means = mean of the population = 10
\n" ); document.write( "std of the sample means = (std of population)/sqrt(n) = 2/sqrt(25) = 2/5
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\n" ); document.write( " Using the above distribution find the probability of a score less than 11
\n" ); document.write( "Assuming that 11 is a score and not a sample mean::
\n" ); document.write( "z(11) = (11-10)/2 = 1/2
\n" ); document.write( "P(x < 11) = P(z < 1/2) = 0.6915
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\n" ); document.write( "Assuming that 11 is sample mean::
\n" ); document.write( "z(11) = (11-10)/[2/sqrt(25)] = 1/[2/5] = 2.5
\n" ); document.write( "P(x < 11) = P(z < 2.5) = 0.9938
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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