Mimi plans on growing tomatoes in her garden. She has 20 cherry tomato seeds. Ba

Question

Mimi plans on growing tomatoes in her garden. She has 20 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.60.

(a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that she gets at least 15 cherry tomato seedlings. (round the answer to 3 decimal places) Show all work.

Explanation / Answer

a) n = 20

p = 0.6

q = 1 - 0.6 = 0.4

b) P(X = x) = 20Cx * 0.6x * 0.420-x

P(X > 15) = P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)

                = 20C15 * 0.615 * 0.45 + 20C16 * 0.616 * 0.44 + 20C17 * 0.617 * 0.43 + 20C18 * 0.618 * 0.42 + 20C19 * 0.619 * 0.41 + 20C20 * 0.620 * 0.40

                = 0.126

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