Question

For the following distribution:

The parameters for this probability distribution best match the parameters of:

a. Binomial distribution with n=4, π = 0.4
b. Normal distribution with n=4, π = 0.4
c. Hypergeometric distribution with n=4, π = 0.6
d. Binomial distribution with n=30, π = 0.5

Answer 1

The parameters for this probability distribution best match the parameters of:

a. Binomial distribution with n=4, π = 0.4

Step-by-step explanation:

The given distribution is likely a binomial distribution, as it involves a fixed number of independent trials with only two possible outcomes. The parameters provided, n=4 (number of trials) and π=0.4 (probability of success), align with the characteristics of a binomial distribution. The binomial distribution is used when there are a fixed number of trials, each with the same probability of success.

In a binomial distribution, the probability mass function (PMF) is given by:

`\[ P(X=k) = \binom{n}{k} \cdot π^k \cdot (1-π)^(n-k) \]`

Where:

-
`\(\binom{n}{k}\)` is the binomial coefficient, representing the number of ways to choose k successes out of n trials.

- π is the probability of success in a single trial.

- n is the number of trials.

- k is the number of successes.

In this case, with n=4 and π=0.4, the distribution's PMF can be calculated using the provided parameters.

Given the characteristics of the distribution and the parameters specified, it becomes evident that the most suitable option is the binomial distribution with n=4 and π=0.4 (Option A). This distribution is a fitting model for scenarios involving a fixed number of independent trials with a consistent probability of success.