>> = .1586 probability that the machine will overflow an 8 oz c.

Correct. Using the cumulative distribution function for normal distributions :

Phi(x) = [ 1 + erf((x - mu) / (sigma * sqrt(2))) ] / 2

with x = 8, mu = 7.6 and sigma = 0.4

>> (b) Estimate the probability that the machine will not overflow an 8 oz cup

>> = .8585 probability that the machine will not overflow an 8 oz cup

This is the inverse of the result from (a), so 1 - 0.1586 = ...

>> (c) The machine just been loaded with 850 cups. How many of these do you expect will overflow when served?

Use the probability calculated in (a) for this ...