Question

A student takes a true-false test that has 12 questions and guesses randomly at each answer. let x be the number of questions answered correctly. find p(x=5)

a. 0.1934
b. 0.2256
c. 0.1208
d. 0.0002

Answer 1

The correct answer is a) 0.1934.

The binomial distribution is

`(_k^n)p^k(1-p)^(n-k)`, where n is the number of trials (questions), k is the number of successes (correct answers), and p is the probability of a success (0.5 on true-false questions). Using our information we have:


`(_5^(12))(0.5)^5(1-0.5)^(12-5) \\ \\=(_5^(12))(0.5)^5(0.5)^7 \\ \\=(12!)/(5!7!)(0.5)^5(0.5)^7 \\ \\=792(0.5)^5(0.5)^7 \\=0.1934`