Answer to Question #224804 in Statistics and Probability for Bernice

Question

Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by 0.5. 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=15, p=0.5.

$P(X<4)=\Sigma_{i=0}^3C_7^i0.5^i0.5^{15-i}=0.0176.$