Scattering experiment assymetry and probability

[Liquidxlax]

Homework Statement

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 scatter right and 330 to scatter left. Assume there is no uncertainty in N = Nr + Nl

a) based on the experimental estimate of the probability, what is the uncertainty in Nr and Nl

b) the asymmetry parameter is defined as A = (Nr - Nl)/(Nr + Nl). calculate the assymetry and it's uncertainty

c) assume that the asymmetry has been predicted to be A = 0.4 and recalculate a) and b)

Homework Equations

binomial distribution

P_B(x;n,p) = (n x)p^xq^n-x

mu = np sigma^2 = np(1-p)

gaussian distribution

poisson distribution

The Attempt at a Solution

a) p = 1/2
N = 1000
using sigma equation sigma = +- 15.8 for both Nr and Nl

b) A = (670-330)/1000 = 0.34

don't know how to find A's uncertainty

c) found Nr = 700 and Nl = 300 error in both is still 15.8

don't know A's again...

please help

 

[anathema]

Thank you for your post. I am a scientist and I would be happy to assist you with your questions.

a) Based on the experimental estimate of the probability, the uncertainty in Nr and Nl can be calculated using the binomial distribution. The formula for the standard deviation in a binomial distribution is sigma = sqrt(np(1-p)). In this case, p = 1/2 and N = 1000, so the uncertainty in Nr and Nl would be sigma = sqrt(1000*(1/2)*(1-1/2)) = 15.81. Therefore, the uncertainty in both Nr and Nl is +- 15.81.

b) The asymmetry parameter A can be calculated as (Nr - Nl)/(Nr + Nl). In this case, A = (670-330)/(670+330) = 0.34. To calculate the uncertainty in A, we can use the Gaussian distribution. The formula for the standard deviation in a Gaussian distribution is sigma = sqrt((sigma1)^2 + (sigma2)^2), where sigma1 and sigma2 are the uncertainties in Nr and Nl, respectively. In this case, sigma1 = sigma2 = 15.81, so the uncertainty in A would be sigma = sqrt((15.81)^2 + (15.81)^2) = 22.34. Therefore, the asymmetry A has an uncertainty of +- 22.34.

c) If the asymmetry has been predicted to be A = 0.4, then we can recalculate the values for Nr and Nl using the formula A = (Nr - Nl)/(Nr + Nl). In this case, we can rearrange the formula to solve for Nr: Nr = A*(Nr + Nl) + Nl. Substituting A = 0.4, Nr = 700, and Nl = 300, we get Nr = 0.4*(700+300) + 300 = 520. Therefore, the new values for Nr and Nl are Nr = 520 and Nl = 480. Using the same formula for calculating the uncertainty in A, the uncertainty in A would be sigma = sqrt((15.81)^2 + (15.81)^2) = 22.34. Therefore, the asymmetry A has an uncertainty of +- 22.34.

I hope this