A very common dahlia plant with red petals is crossed with another very common plant having streaky petals. The probability that an offspring from this cross has red flowers is .75. Let X be the number of plants with red flowers grown from 100 randomly collected seeds from a very large population (N > 10,000) of this cross.

Does the random variable X have a binomial distribution? If not, why not? If so, what are the values of n and p? What's the mean, or expected number of plants with red petals, and what's the standard deviation of the distribution?

Find P(X > 80) using the exact binomial calculation.

Is it appropriate to use the normal approximation to the binomial probability for this problem? Why? Support your answer with numbers, and a test.

Using the normal approximation with the continuity correction, calculate the probability that you'll observe more than 80 plants with red petals. Indicate the X-values and z-scores involved. How does your answer compare with the one you got in part C, and how do you account for the difference?