The highest grade for Florida oranges is U. S. Fancy and is based principally on color. Suppose that Shannon owns a small organic orchard and that the proportion of oranges she grows which can be classified as U. S. Fancy is 0.40. One morning, Shannon randomly picks 44 oranges. Estimate the probability that the number of oranges that will be classified as U. S. Fancy, X, is fewer than 16.

Use a normal approximation to the binomial distribution with continuity correction to obtain the solution. Give your answer precise to at least four decimal places