Suppose I know only -5 <= X <= 95 with Xmean = 75.
I believe that means that P(-5 <= X <= 75) = 20% and
P(75 <= X <= 95) = 80%, roughly. Right?

1. Suppose that I believe X is uniformly distributed in
each subrange. Then I could generate random X by:

X = if RAND() <= .20 then -5 + 80*RAND() else 75 + 20*RAND()

Is there a more elegant formulation? Perhaps a
closed-form expression, something of the form
(which is obviously wrong):

X = -5 + 80*RAND() + 20*RAND()

2. Suppose that I believe X is "nearly normally" distributed
across the range [-5,95], but with a left skew that pulls
the mean to the right.

How would I generate random X? Perhaps
something of the form (which is obviously wrong):

X = NORMINV(RAND(), 75, 12.5)

where 12.5 = (95-(-5))/8 is the approximate sd
(z = 4) if the mean were 45 ((-5+95)/2).

(There probably is not just one answer, since I said
nothing about the kurtosis. Frankly, I know nothing
about kurtosis. Assume the same kurtosis as a standard
normal curve or whatever other simplifying assumption
makes sense.)