Binomial Distribution and Normal Approximation: Evaluating Mendel's Proportion of Long Stemmed Plants

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Binomial Distribution and Normal Approximation: Evaluating Mendel's Proportion of Long Stemmed Plants In one of Mendel's experiments with plants, 1064 offspring consisted of 787 plants with long stems. According to Mendel's theory, 3/4 of the offspring plants should have long stems. Assuming that Mendel's proportion of 3/4 is correct, find the probability of getting 787or fewer plants with long stems among 1064 offspring plants. Based on the result, is 787 offspring plants with long stems unusually low? What does the result imply about Mendel's claimed proportion of 3/4? Solution: We have n = 1064 and p = 0.75 Since np = 1064*0.75 = 798 and n (1 - p) = 1064*0.25 = 266 are greater 5, we use normal approximation to binomial Mean, J = np = 1064*0.75 = 798 Standard deviation, 0 = Vnp(1 - p) = V1064*0.75%0.25 = 14.124 Using continuity correction, + StudyXY
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