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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the population mean is 65
the population standard deviation is 2.
the sample size is 100
the standard error is 2/sqrt(100) = 2/10 = .2
you want to find the probability that the average age of the population will be between 64 and 66 years of age.
z1 = (64 - 65) / .2 = -1/.2 = -5.
z2 = (66 - 65) .2 = 1/.2 = 5.
the area under the normal distribution curve between a z-score of -5 and 5 is equal to .9999994258.
that's equal to 100% when you round to as many as 5 decimal places.
the key to obtaining the z-score is calculating the standard error, which is the standard deviation of the distribution of sample means.
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.
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