Bin-Geom-activity (1).docx - Word antoinne gary X File Home Insert Design Layout References Mailings Review View Help Tell me what you want to do & Share Lucky Guess? Quiz 9 Quiz 10 Binomial Distribution Activity Imagine this scenario: You've just walked into your first class on a Monday morning, and your professor announces a 10-question true-or-false quiz. You haven't been keeping up with the material for class - you wouldn't do that, would you?! - so you're panicking a bit. You decide that your best bet is to simply guess on all ten questions, since you've got a 50% chance of getting a question right. If "success" is defined as getting a correct answer and "failure" is defined as getting an incorrect answer, then P(success) = p = 0.5 and P(failure) = q = 0.5. We define the random variable X as the number of correct answers. The random variable has possible values x = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10). We will simulate taking the quiz and determine the long-term relative frequency where you get 7 questions correct - that is, P(X= 7) Correct: Correct: 1. You will need to pretend to take this quiz 10 times. You will check your answers with the provided answer key. Keep track of the number of correct responses. When completed, come to the board and provide your results. Using the cumulative results from the entire 2. Do the same thing as before but use your calculator to simulate the quiz. Use the following class, calculate the frequency of the event "getting exactly 7 questions correct," P(X"= 7). convention: 1 = correct answer, 0 = incorrect answer. On your calculator, enter the command randint(0, 1, 10). This instructs the calculator to randomly choose a set of 10 Quiz 1 Quiz 2 Quiz 3 Quiz 4 numbers that are either 1 or 0. For example, the outcome (0, 1, 1, 0, 1, 1, 0, 1, 0, 1) is "incorrect, correct, correct, incorrect, correct, correct, incorrect, correct, incorrect, correct" for 6 correct responses. Continue to press ENTER until you have 50 trials. Use a tally mark to record each time you observe exactly 7 correct answers. Calculate the relative frequency for the event "exactly 7 correct answers." n = trials # of "exactly 7 correct" quizzes =. relative frequency of "exactly 7 correct" quizzes = 3. Do the results of your simulation come close to the theoretical value for P(X = 7)? To Correct: Correct: Correct: Correct: check this, calculate the binomial probability of "exactly 7 correct answers" using the calculator function binom pdf(x, p, x) = binom pdf (10, 0.5, 7). Quiz 5 Quiz 6 Quiz 7 Quiz 8 Correct: Correct: Correct: Correct: Page 1 of 3 1054 words - - + 80%Bin-Geom-activity (1).docx - Word antoinne gary X File Home Insert Design Layout References Mailings Review View Help Tell me what you want to do & Share Cereal Cash Geometric Distribution Activity In 1986-1987, Cheerios cereal boxes displayed a dollar bill on the front of the box and a cartoon character who said, "Free $1 bill in every 20th box!" We want to simulate an experiment to determine the number of boxes of Cheerios you would expect to buy in order to get one of the "free" dollar bills. 1. Let a two-digit number (00 to 99) represent a box of Cheerios. What digits would you use to represent a box of Cheerios with a $1 in it? What digits would you then use to represent boxes without the $1 in it? boxes with $1 bill boxes without $1 bill 2. Indicate which random number table you are given (using the letter and number at the bottom of the page) and indicate on which row you begin your counting. Write down the pairs of numbers and tally the number of trials it takes until you get a box with a $1 bill in it. How many boxes did you have to buy in order to get one with a $1 bill in it? If you do not usually buy Cheerios, would this promotion induce you to buy a box in hopes of getting one with a dollar in it? table # row # number pairs: 3. Now use your calculator in a similar way to how we found random numbers in the first activity. Use whole numbers 1, 2, 3, 4, 5 to indicate "$1 in box" and whole numbers 6 through 100 to indicate "no bill in box." On your calculator, enter the command randint(1, 100, 1). This instructs the calculator to randomly choose a single number between 1 and 100, inclusive. The outcomes 1-5 are successes and the outcomes 6-100 are failures. Continue to press ENTER and count how many boxes of Cheerios you would need to purchase until you get a box with a $1 bill in it. Do this experiment 20 times. Calculate the mean number of boxes until you get a dollar bill. Compare to the definition of the mean for a geometric probability distribution (). mean # of boxes to get $1 H= Page 3 of 3 1054 words - - + 80%