SOLUTION: certain length measurement is performed 100 times The arithmetic mean reading is 10.85 m, and the standard deviation 0.01 m.
How many readings fall within (a) +- 0.001 meters, (b
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-> SOLUTION: certain length measurement is performed 100 times The arithmetic mean reading is 10.85 m, and the standard deviation 0.01 m.
How many readings fall within (a) +- 0.001 meters, (b
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Question 1176482: certain length measurement is performed 100 times The arithmetic mean reading is 10.85 m, and the standard deviation 0.01 m.
How many readings fall within (a) +- 0.001 meters, (b) +- 0.01 meters, and (c) +- 0.1 meters from the mean value?
Also, calculate the tolerance limits for 90 and 95 percent confidence level. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the number of measurements is 100.
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.
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.
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:
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
