# Standard deviations and probabilities

1. Nov 14, 2007

### Sir

1. The problem statement, all variables and given/known data
Suppose a sample containing 0.600 ppm Selenium is analyzed by a method for which the standard deviation of the population is known to be 0.005 ppm.
1) What is the the probability that a single determination would return a value less than 0.590 ppm?
2) What is the probability that the average for 4 determinations would be less than 0.590 ppm?

2. Relevant equations
the table at the bottom of http://64.233.167.104/custom?q=cache:bdW_K0aRhzEJ:www.palgrave.com/business/taylor/taylor1/lecturers/lectures/handouts/hChap5.doc+chart+area+beneath+normal+curve+standard+deviations&hl=en&ct=clnk&cd=7&client=pub-8993703457585266" [Broken]page tells the area under a normal curve for different standard deviations.

3. The attempt at a solution
for 1) we look on the table for 2.0 standard deviations below the mean, and see that the area under the curve is 0.4772. and at infinite standard deviations, the area is necessarily 0.5000.
so to return a value in this range (less than 0.590 ppm) the solution is ( 0.5 - 0.4772 ) * 100%
= 2.28%

for 2) i don't even know where to start. the answer given is 0.0032%. this table doesn't go far enough, but the probability of finding a value less than 0.580 (or 4 standard deviations below) is 0.0032%. I don't know whether that is relevant or not.
the internets and my textbook combined were less than helpful on this as well.

thanks.

Last edited by a moderator: May 3, 2017
2. Nov 15, 2007

### Sir

all right! I found the equation to govern this.

let z be the number of standard deviations away from the mean
... u be the mean
... x be the value of a determination
... n be the number of determinations
... s be the standard deviation

z = (| u - x | * (n)^(1/2)) / s