(Solution) - Find the binomial distribution and its normal approximation for the -(2025 Original AI-Free Solution)

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Find the binomial distribution and its normal approximation for the number of intermediate offspring. What is the probability of getting eight or fewer?
Suppose that the alleles A and a for height are additive, meaning that plants with genotype AA are tall, plants with genotype Aa are intermediate, and those with genotype aa are short. If an Aa plant is crossed with another Aa plant, 1/4 of the offspring should be tall, 1/2 should be intermediate, and 1/4 should be short. Assuming that the other conditions for the binomial distribution are met, find the probabilities of the following. Suppose such a cross produces 36 offspring.