# Probability Distributions and asymmetry

1. Oct 3, 2011

### Liquidxlax

1. The problem statement, all variables and given/known data

In a scattering experiment to measure the polarization of an elementary particle, a total of N = 1000 particles was scattered from a target. of these, 670 were observed to scattered to the right and 330 to the left. Assume there is no uncertainty in NL + NR = 1000

a) based on the experimental estimate of the probability, what is the uncertainty in NL and NR?

b) The asymmetry parameter is defined as A = (NL - NR)/(NL + NR). Calculate the asymmetry and its uncertainty

c) Assume that the asymmetry has been predicted to be A= 0.4, find a) and b) with the new value.

2. Relevant equations

σ = sqrt(Np(1-p) where p is the probability of the outcome and σ is the deviation N is the total number of trials

3. The attempt at a solution

N = 1000 and p = 1/2 so the uncertainty σ in NL and NR is ±15.8

simple plug and chug as well as the asymmetry

which equals 0.34

The problem i'm having is calculating the uncertainty in the asymmetry since the problem states there is no uncertainty in N.

I was thinking that maybe it would be

R + σL)/1000 but then that would mean that the error in the uncertainty would not change.

for part c) the new values of NL = 300 ±15.8 and NR = 700 ± 15.8