the mean is 10.85 meters.
the standard deviation is .01 meters.
this is not a sample.
this is the population.
use the z-score formula to find the number of standard deviations from the mean.
the z-score formula is z = (x - m) / s
z is the z-score
x is the raw score
m is the raw mean
s is the standard deviation in this case bcause we are dealing with a population.
if the score is plus or minus .001 meters from the mean, then the low z-score and high z-score are calculated as follows.
low z-score = -.001 / .01 = -.1
high z-score = .001 / .01 = .1
the ratio of measurements between plus or minus .001 from the mean would therefore be equal to .0796557923.
the percent is equal to 100 times that = 7.97% rounded to 2 decimal places.
if the score is plus or minus .01 meters from the mean, then the low z-score and high z-score are calculated as follows.
low z-score = -.01 / .01 = -1
high z-score = .01 / .01 = 1
the ratio of measurements between plus or minus .01 from the mean would therefore be equal to .6826894809.
the percent is equal to 100 times that = 68.27% rounded to 2 decimal places.
if the score is plus or minus .1 meters from the mean, then the low z=score and high z-score are calculated as follows:
low z-score = -.1 /.01 = -10
high z-score = .1 / .01 = .10
the ratio of measurements between plus or minus .1 from the mean would therefore be equal to 1,
the percent is equal to 100 times that = 100%.
at two tailed confidence level of 90%, the low and high z-scores would be equal to plus or minus 1.645 rounded to 3 decimal places.
the low raw score is found by the following formula:
-1.645 = (x - 10.85) / .01
solve for x to get:
x = .01 * -1.645 + 10.85 = 10.83355
the high raw score is found by the following formula:
1.645 = (x - 10.85) / .01
solve for x to get:
x = .01 * 1.645 + 10.85 = 10.86645
at 95% confidence interval, the low and high z-scores would be equal to plus or minus 1.960 rounded to 3 decimal places = 1.96 rounded to 2 decimal places.
the low raw score is found by the following formula:
-1.96 = (x - 10.85) / .01
solve for x to get:
x = .01 * -1.96 + 10.85 = 10.8304
the high raw score is found by the following formula:
1.96 = (x - 10.85) / .01
solve for x to get:
x = .01 * 1.96 + 10.85 = 10.8696
visually, these look like as follows:
