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You should only perform a linear interpolation, in my opinion. For instance,
dat - structure(list(probs = c(0.06, 0.1, 0.2, 0.24, 0.3, 0.5, 0.7, 0.89, 1); x = c(-120, 100, 97, 90, 80, 70, -60, -50, -40)), class = "data.frame", row.names = c(NA, -9L))
c(0.1, 0.15, 0.2) #> fn - approxfun(dat$probs, dat$x) [1] -100.0 -98.5 -97.0