document.write( "Question 1182108: What is the probability that a sample mean calculated from a sample of 100 individuals from the Florida subdivision will have an average age between 64 and 66 years of age. As in question #2, the mean age of the population is 65 years of age, and the standard deviation is 2 years. For this problem, be sure to use the z-calculation that is for sample means. \n" ); document.write( "
Algebra.Com's Answer #814545 by Theo(13342)\"\" \"About 
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the population mean is 65
\n" ); document.write( "the population standard deviation is 2.
\n" ); document.write( "the sample size is 100
\n" ); document.write( "the standard error is 2/sqrt(100) = 2/10 = .2
\n" ); document.write( "you want to find the probability that the average age of the population will be between 64 and 66 years of age.
\n" ); document.write( "z1 = (64 - 65) / .2 = -1/.2 = -5.
\n" ); document.write( "z2 = (66 - 65) .2 = 1/.2 = 5.
\n" ); document.write( "the area under the normal distribution curve between a z-score of -5 and 5 is equal to .9999994258.
\n" ); document.write( "that's equal to 100% when you round to as many as 5 decimal places.\r
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\n" ); document.write( "\n" ); document.write( "the key to obtaining the z-score is calculating the standard error, which is the standard deviation of the distribution of sample means.
\n" ); document.write( "that standard error is equal to the standard deviation of the population divided by the square root of the sample size, which is 2 / sqrt(100) = 2/10 = .2.\r
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