# Probability: ranges in Gaussian approximation

1. Feb 7, 2006

### mmh37

Hello everyone,

I got stuck on a probability question and would be very thankful if someone could give me a hint:

An Opaque bag contains 10 green counters and 20 red. One couner is selected at random and then replaced: green scores 1 and red scores zero.

1) Calculate the probability of obtaining scores in the ranges <r> +/- 0.5* root(var(x)) and <r> +/- root(var(x))

that doesn't seem too bad. for the variance and the mean I got 2.22 and 1.66 respectively, so the ranges are:

a) from 0.66 to 2.32, so I just add P(1) + P(2)= 0.67

b) from .17 to 3.17, so this is P = P(1) + P(2) + P(3)= .823

2) The Gaussian approximation of the binomial distribuion in (1) is given as P(r) = exp [-9(r-5/3)^2/20]; now do the same as in 1 and compare the answers. In what sense is P(r) a good approximation to p?

OK, so I don't know how to go on from here. Help's very mcuh appreciated!

2. Feb 8, 2006

### mmh37

Can anyone help?