Answer to Question #255759 in Statistics and Probability for aki

Question

Assume that random guesses are made for six multiple choice questions on an SAT​ test, so that there are n=6 ​trials, each with probability of success​ (correct) given by p=0.65. Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than 4.

Answer 1

This is a binomial distribution with n=6, p=0.65.

$P(X<4)=\Sigma_{i=0}^3C_6^i0.65^i(1-0.65)^{6-i}=0.3529.$