To find the mean and standard deviation, use this statement from the problem:

Specialty's senior sales forecaster predicted an expected demand of 20,000 units with a 0.95 probability that demand would be between 10,000 units and 30,000 units.

This is saying that the 95% confidence interval for this product is 20,000 +/- 10,000.

Considering that a 100(1-a)% CI has the form mean +/- z[a/2]*sd, you can pick out what "mean" is in your problem, and determine sd (the standard deviation) using z[a/2] = z[.025] = 1.96

Let X = # of toys sold.

In the case where 15,000 (or any quantity Q) are shipped,

P[stock-out] = P[X > 15,000]

Since X is assumed to be normal, next you'll want to standardize X, and then do that stuff with the z-values.

=P[ Z > (15,000 - mean)/sd ] = 1 - Phi( (15,000-mean)/sd )