Question

In: Statistics and Probability

The SAT is a standardized college admissions test used in the United States. The following two...

The SAT is a standardized college admissions test used in the United States. The following two multi-part questions will ask you some questions about SAT testing.

This is a 6-part question asking you to determine some probabilities of what happens when a student guessed for all of their answers on the SAT. Use the information below to inform your answers for the following questions.

An old version of the SAT college had a -0.25 point penalty for every incorrect answer and awarded 1 point for a correct answer. The quantitative test consisted of 44 multiple-choice questions each with 5 answer choices. Suppose a student chooses answers by guessing for all questions on the test.

1. What is the standard error of guessing on all 44 questions? Use the Central Limit Theorem to determine the probability that a guessing student scores 8 points or higher on the test.

Solutions

Expert Solution

The quantitative test consisted of n=44 multiple-choice questions each with 5 answer choices each.

If you are guessing than the probability that you get the answer correct is

If you are guessing than the probability that you get the answer incorrect is

This probability is independent and the same for every question.

This is an example of the binomial distribution, we shall be using the formula for the normal approximation of binomial distribution.

the expected value of points for guessing on one question =

the expected score of guessing on all 44 questions =

the standard error of guessing on all 44 questions =

the probability that a guessing student scores 8 points or higher on the test

orchestra answered 1 year ago
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