A student guesses on every question of a test that has 10 multiple-choice questi

Question

A student guesses on every question of a test that has 10 multiple-choice questions (each with five choices) and 10 true-false questions. A student’s guess on any question is independent of the guess he/she made on any other question. Suppose X represents the number of questions on the test that a student who is guessing on every question gets right. Is a Binomial Distribution an appropriate model for this discrete random variable X ? Why or why not? Check the requisite conditions: Randomization, Independence, 10% Condition, Fixed Number of Trials, Two Outcomes per Trial.

Explanation / Answer

Yes. Binomial Distribution an appropriate model for this discrete random variable X.

Because on each of the true/false questions, the student has a 1/2 or 0.5 chance of guessing correctly. Since the questions are all independent.

A random variable is binomial if the following four conditions are met:

There are a fixed number of trials (n). In this n=10

Each trial has two possible outcomes: success or failure. In this true or false

The probability of success (call it p) is the same for each trial. Here p=0.5

The trials are independent, meaning the outcome of one trial doesn't influence the outcome of any other trial.

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