Question 5, 5.2.17-T HW Score: 28.57%, 4 of 14 points multipl View an example | All parts showing answer Assume that random guesses are made for twelve multiple choice questions on an SAT test, so that there are n=12 trials, each with probability of success (correct) given by p=0.45. Find the indicated pa for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4. The probability of obtaining x successes in n independent trials of a procedure that follows a binomial distribution, where the probability of success is p, is given by the following formula P(x)=nCxp*(1-p)*, x=0,1,2 n The phrase fewer than means "less than." The values of the random variable X less than 4 are 3, 2, 1 and 0. P(X<4)= P(3 or 2 or 1 or 0) = P(3) + P(2) + P(1) + P(0) Use technology to find each probability, rounding to six decimal places as needed. P(3)=0.092326 P(2)=0.033853 P(1)=0.007523 P(0)=0.000766 Sum these probabilities to find P(X<4), rounding to four decimal places. 0.092326+0.033853+0.007523+0.000766-0.1345 Thus, P(X<4)= 0.1345 There is a 0.1345 probability that, in a random sample size of 12, there will be fewer than 4 correct answers Close Print Get more help - an example

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