Question

describe an example that uses discrete probabilities or distributions. Provide an example that follows either the binomial probabilities or any discrete probability distribution, and explain why that example follows that distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then show the work (or describe the technology steps) and solve that probability example.

Answer 1

Example of binomial distribution

Suppose that 10 seeds of Brand A were planted one in each pot and let X_i  = 1 or 0 according as the seed in the i^th pot germinates or not.

The data consists of (x₁ , ....x₁₀) a sequence of ones and zeroes and is regarded as a realization of (X₁, ...X₁₀) such that components are independent and identically distributed (i.i.d) random variables with P(X_i = 1) = p and P(X₁ = 0) = 1- p

Suppose we want to find probability that in a batch of 10 seeds exactly 8 seeds will germinate

and suppose that the probability of a seed is germinate is .90

Then using the following Binomial command to find the above probability is

=BINOMDIST(8,10,0.9,0)

The syntax in the bracket of the Binomial distribution is as P( x, n, p, cumulative)

In the above example x = 8, n = 10, p = 0.9 and cumulative = 1 since we want to find exact probability.

Also suppose we want to find the probability of at least 15 seeds are germinate then the excel commands is as follow.

=1 -BINOMDIST(14,20, 0.9, 1) = 0.9887

Since he probability of at least 15 seeds are germinate P(X >=15) = 1 - P(X < 15) = 1- P(X < = 14)