Question 1182108
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.