Question

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 expected value of points for guessing on one question?What is the expected score of guessing on all 44 questions?

Answer 1

(i)

From the given data, the followong Table is calculated:

Event	Value (x)	Probability (p)	x.p
Answering correctly by guessing one question	1	1/5 = 0.2	1 X 0.2 = 0.2
Answering incorrectly by guessing one question	- 0.25	4/5=0.8	- 0.25 X 0.8 = - 0.2
Total = the expected value of points for guessing on one question			0.2 - 0.2 = 0So,

So,

the expected value of points for guessing on one question = 0

So,

Answer is:

0

(ii)

the expected value of points for guessing all 44 questions = 44 X 0= 0

So,

Answer is:

0