Question

Let x represent the number of correct responses on the test. (a) What kind of probability distribution does x have?

a) geometric
b) binomial

Answer 1

The probability distribution of X, representing the number of correct responses on the test, is a binomial distribution.

Step-by-step explanation:

The random variable X represents the number of correct responses on the test. To determine the probability distribution of X, we need to consider the characteristics of the experiment. In this case:

1. There are multiple independent trials (questions on the test).
2. Each trial has two possible outcomes: a correct response (success) or an incorrect response (failure).
3. The probability of success (p) and failure (q) remains the same for each trial.

Based on these characteristics, we can conclude that the probability distribution of X is a binomial distribution.