1. In an experiment, there are n independent trials. For each trial, there are t

Question

1. In an experiment, there are n independent trials. For each trial, there are three outcomes A, B, and C. For each trial, the probability of outcome A is 0.40; the probability of outcome B is 0.50; and the probability of outcome C is 0.10. Suppose there are 10 trials. Can we use the binomial model to determine the probability of four outcomes of type A, five of type B, and one of type C? Explain 2. A biologist is studying a new hybrid tomato. It is known that the seeds of this hybrid tomato have probability of 70% of germinating. The biologist plants six seeds. What is the probability that exactly four seeds wil germinate? (Show formula) Find the mean and variance.

Explanation / Answer

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2) n = 6

p = 0.7

Mean = n * p = 6 * 0.7 = 4.2

VAr = (n * p * q) where q = 1 - p

Var = (6 * 0.7 * 0.3) = 1.26

Now,

P(X = 4) = 6C4 * 0.7^4 * 0.3^2

P = 0.324

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