Probability of agreeing to do some work depending on the payment I am looking for several options of modeling the probability of people agreeing to do some work depending on the price/payment. The payment can only range between p1 and p2 (p1 < p2). I looked at normal distribution and not sure if I can use it to model my case because the higher the payment, the higher probability that people will do it, intuitively, therefore it's monotonic. Is there anyway to only use the left side of the normal distribution to preserve the monotonicity?
Any other suggestions would be appreciated. 
THanks.
 A: Here is the cumulative distribution function (CDF) of a Gaussian with mean $\mu = (p1+p2)/2$ and variance $\sigma = (p2-p1)/6$, which is of course monotonic in price (as all CDFs must be):

A: Because you have a bounded pay scale, and you do not know the shape of the function that maps probability of acceptance against pay, this is an excellent use case for a  generalized additive model, in particular a generalized additive logistic regression model. For this, I recommend the gam function from the R package mgcv. If you have multiple responses from the same individuals, you can use the gamm function, which allows you to specify random intercepts. You can then use the predict function to compute the fitted probabilities of acceptance for a grid of values on the pay scale. Then you can look at the plot of the curve and decide whether you could describe the relationship using some parametric function with interpretable parameters. If so, you could use one of the many R packages for nonlinear regression modeling to estimate the values of the parameters of that function.
