1.

What values symmetrically enclose 90 and 99% of the area under a Normal curve?

2.

An unbiased analytical system is used to measure an analyte whose true value for the parameter measured is 100 units. If the standard deviation of repeated measurements is 0.80 units, what fraction of measurements will be further than one unit from the true value? Note that this fraction will also be the probability that a single measurement will produce a test result which is either less than 99 or greater than 101, when the material is measured. What fraction of measurements will be further than 1.5 units from the true value? Give the answers to two decimal places.

1.

The required values are 1.645 and 2.575, but two decimal places are commonly used.

2.

The fraction further than 1 unit from the true value is 0.21; the fraction further than 1.5 units is 0.06.

3.

Calculate by hand the standard deviation of the three numbers 5, 6, 7. If you do not get the answer 1 - do it again! Now check that your calculator, spreadsheet and statistical package give that answer.

Note that the three deviations from x sum to zero, i.e., ( x _i - x) = 0. This is always the case for deviations about the sample mean. Therefore, once n-1 deviations are determined, the value for the last one must be such that the sum equals zero. Thus, only n-1...