Answer to Question #247336 in Statistics and Probability for sherryl

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 p=0.55. Find the indicated probability for the number of correct answers.

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

P(X<4)=

nothing

​(Round to four decimal places as​ needed.)

Answer 1

It is binomial distribution.

n = 7

p = 0.55

P(x < 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x = 0) = C(7, 0) 0.55⁰ (1 – 0.55)^{7 – 0}

             = 0.00373669453125

P( x < 4) = 0.00373669453125+0.03196949765625+0.11722149140625+0.23878451953125 = 0.391712203125 = 0.3917