Advanced Placement (AP)

Have you ever been tempted to try the claw machine to win a prize? Today we will work problems aboutthe claw machine.Part 1: Simulation. For one style of claw machine, the pressure the claw squeezes with changes for each trial. The top psi level only appears 1/18 of the time. The claw has enough psi to lift the prize 1/9 of the time. Use the random digits below to simulate the number of wins in 5 trials of the claw game. Repeat this until 25 samples have been taken to find the expected number of wins in 5 trials of the game.Part 2: Given the true proportion of winning on one trial is 1/9, then find the chance of winning at least once in 5 trials.Part 3: How many trials should a player expect to play before winning a prize?Part 4: What is the chance that the first win occurs in fewer than 4 trials?Part 5: How many trials are required before the users chance of success reaches at least 0.5?Standardized Tests Part 1: A student reads a passage and answers questions based the passage for 3 minutes. Each question has three possible answers from which to choose. The student answers 22 questions and 11 are correct. The teacher assumes the student guessed on the questions.What is the expected score for a student who is guessing?What is the standard error out of 22 questions for a student who is guessing?What is the probability of scoring 11 correct if the student is truly guessing?Create a 95% confidence interval for a single trial of the test.What do you tell the teacher about whether they should conclude the student was guessing?