A State-Wide Math Test Consists of 50 True/False Questions and 40

Essay

A state-wide math test consists of 50 True/False questions and 40 multiple choicequestions with 5 answer options. The total score (TS) is equal to the number oftrue/false items correct plus twice the number of multiple-choice items correct.a) For students who are randomly guessing, the distribution of scores on the 500.50. If we define the random variable T = score from T/F items, what are the meanand standard deviation of T for students who are guessing?
b) For students who are randomly guessing, the distribution of scores on the 40 multiplechoice questions is a binomial distribution with probability of success equal to 0.20.If we define the random variable M = score from multiple choice items, what are themean and standard deviation of M for students who are guessing?
c) The total score, TS, is a random variable formed by calculating TM+ 2 . Using yourresults from parts (a) and (b), find the mean and standard deviation of the randomvariable TS.d) For students who randomly guess on the multiple choice part of the test, what is theprobability that the first question correct is the 4th question?