3 AKS 11 A news show displays the results of a poll for a two candidate runoff election between two candidates A and B The polls show that candidate A is leading with 56 of the vote In small print below to poll results it says 6 1 Can candidate A be predicted as the winner Why 4 AKS 1f Sophia earned a score of 35 on Exam A that had a mean of 30 and a standard deviation of 5 She is about to take Exam B that has a mean of 700 and a standard deviation of 25 How well must Sophia score on Exam B in order to do equivalently well as she did on Exam A Assume that scores on each exam are normally distributed 5 AKS 1h John is playing dungeons and dragons with his friends but he is suspicious that one of his friends Mike is cheating In dungeons and dragons you must roll a 20 sided die Typically rolling a 20 is the best roll while rolling a one is the worst All dice rolls are supposed to be random meaning that you have an equal chance of rolling any number John believes that Mike is rolling 20 too frequently for it to be a random occurrence and that Mike must have somehow altered his die a What is the probability that you will roll a 20 if the dice is truly random b John takes Mike s 20 sided die and proceeds to roll it 200 times He records each roll and finds that 12 of the time he rolled a 20 Based on this data he then calculates the margin of error for a 95 confidence interval to be 5 After setting up a confidence interval is it likely that Mike is cheating