(a) To find the percentage of eggs classified as small, we calculate the probability that an egg weighs less than 76 grams. Using the standardization formula:

\(P(X < 76) = P\left(Z < \frac{76 - 80.5}{6.6}\right)\)

\(= P(Z < -0.6818) = 1 - \Phi(0.6818)\)

\(= 1 - 0.7524 = 0.2476\)

Thus, the percentage is 24.8%.

(b) To find the least possible weight of a large egg, we first find the percentage of large eggs:

\(\text{Percentage of large eggs} = 100 - 40 - 24.76 = 35.24\)

We then find the weight corresponding to the cumulative probability of 0.6476:

\(P(Z > x) = 0.6476\)

\(\frac{x - 80.5}{6.6} = 0.378\)

\(x = 80.5 + 0.378 \times 6.6 = 83.0\)

(c) For 150 eggs, the mean number classified as medium is:

\(\text{Mean} = 150 \times 0.4 = 60\)

\(\text{Variance} = 150 \times 0.4 \times 0.6 = 36\)

We approximate the probability that more than 68 eggs are medium:

\(P(X > 68) = P\left(Z > \frac{68.5 - 60}{\sqrt{36}}\right)\)

\(= P(Z > 1.417) = 1 - \Phi(1.417)\)

\(= 1 - 0.9217 = 0.0783\)