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Answer to Question #35210 in Statistics and Probability for pranita

Question #35210
Genetic theory predicts that, in the second generation of a cross of sweet pea plants, blossoms will be either red or white, with each plant having a 3⁄4 chance of producing red blossoms. Blossom colours of separate plants are independent.
Let X be the number of plants with red blossoms out of 12 plants selected at random from the second generation of this cross.
(a) What is the probability distribution of X? [3]
(b) Calculate:
(i) the mean and standard deviation of X. [3] (ii) P(X>8) [2] (iii) P(7≤X≤11) [2]
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