A State Dept

Essay

A State Dept. of Education is writing a state-wide math test, and by law must decide how many points will count as a "failing score." The test consists of 50 True/False questions and 40 multiple choice questions with 5 answer options. The total score (TS) will be equal to the number of true/false items correct plus twice the number of multiple-choice items correct. A decision has been made to make the failing score the score that a student would be expected to get if they randomly guessed on all the questions.
a) If a student is randomly guessing, the 50 True/False questions can be regarded as a binomial chance experiment with probability of success equal to 0.50. If we define the random variable T = score from T/F items, what are the mean and standard deviation of T for a random student who is guessing?
b) If a student is randomly guessing, the 40 multiple choice questions can be regarded as a binomial chance experiment with probability of success equal to 0.20. If we define the random variable M = score from MC items, what are the mean and standard deviation of the M for a random student who is guessing?
c) The total score, TS, is a random variable formed by calculating T + 2M. What are the mean and standard deviation of the random variable TS?
d) If a student is randomly guessing on the multiple choice part of the test, what is the probability that the first multiple choice question correct is the 4th multiple choice question?