Question

4.87 Probability and Statistics (4th Ed.)

I have the following question, with answers provided below and could use a detailed walkthrough of achieving each answer, thank you!

Question: Find the probability that a student can guess correctly the answers to a) 12 or more out of 20, b) 24 or more out of 40, questions on a true-false examination.

Answers:

a) 0.2511 b) 0.1342

Answer 1

Since all questions are true and false so probability of getting a correct answer for one question is

p = P(correct) = 1/2 = 0.5

(a)

Let X is a random variable shows the number of correct answers out of 20. Here X has binomial distribution with parameters as follows:

n =20 and p = 0.5

The probability of getting 12 or more correct answers out of 20 is

(b)

Let X is a random variable shows the number of correct answers out of 40. Here X has binomial distribution with parameters as follows:

n =20 and p = 0.5

The probability of getting 24 or more correct answers out of 40 is