ACTIVITY SET 9 Stat 200 Sections 4 6 Feb 16 Activity 9 1 Work with a partner Use one of the sets of four cards distributed during class Verify that there is one card from each suit hearts diamonds clubs spades in the set Randomly mix the cards and then select one in a way that your partner can t see what you picked Have the partner guess the suit of the card you picked Repeat this 10 times and keep track of right and wrong guesses using the following table Then change places so that you do the guessing and your partner does the card mixing Trial 1 2 3 4 5 6 7 8 9 10 Right or Wrong a What was the number of correct guesses made by your partner If you weren t present for the lab write Not present for your answer we won t hold it against you Number of correct guesses by partner If you did this activity during class please enter the number of correct guesses by your partner into ANGEL using the specified link in the Week 6 folder b Assuming a person randomly guesses each time explain why this is a binomial experiment and give the values of n and p for this experiment c Assuming random guessing what is the expected value mean value of the number of correct guesses in this experiment Show the calculation d Start Minitab from Spreadsheets and Statistics folder of Start menu Use Calc Probability Distributions Binomial At the top of the resulting dialog box click on Probability then enter 10 as number of trials and 0 25 as the probability of success Near the bottom click on Input Constant and enter 0 in the adjacent box This will give the probability of 0 correct guesses after OK is clicked Probability of 0 correct guesses P X 0 e Use Minitab to find separately the probabilities of 1 2 and 3 correct guesses Probability of 1 correct guesses P X 1 Probability of 2 correct guesses P X 2 f Add the probabilities found for 0 1 and 2 to find the cumulative probability P X 2 the probability that the number of correct guesses is 2 or less You can round off the probabilities to 3 decimal places if your wish Probability of 2 or less correct guesses P X 2 g Again use Calc Probability Distributions Binomial NEAR THE TOP click on Cumulative Probability and near the bottom change the Input Constant to 6 This will give the cumulative probability for 6 or less correct guesses Probability of 6 or less correct guesses P X 6 h Using the probability found in part g determine the probability somebody could get more than 6 correct guesses Activity 9 2 In each part explain 1 whether the variable is discrete or continuous AND 2 if it is discrete whether it is a binomial random variable OR if it is continuous whether you think it might be a normal random variable Note the issue of whether it s normal will mainly be a guess on your part Just explain why you think it might or might not be a Weights of all students at Penn State b Number of correct answers on a 30 question multiple choice test for somebody who randomly guesses at every question There are four answer choices for each question c Heights of women at Penn State d A woman buys a lottery ticket every week for which the probability of winning anything at all is 1 10 She continues to buy them until she has won 3 times X the number of tickets she buys e Daily snowfall amounts in State College for all days between December 1 and March 15 Activity 9 3 For a randomly selected sample of n 10 people assume X number of people with type O blood is a binomial random variable with p 0 3 the fraction with type O in the larger population Use Minitab as it was used in activity 9 2 to assist in answering the following a P X 5 the probability that the number of people with type O is exactly 5 b P X 5 the probability that the number with type O is 5 or less Note that this is a cumulative probability c What is the probability that more than 5 people in the sample have type O blood Activity 9 4 Suppose that n 72 is the number of students in attendance for this section 6 today Let s assume that the chance any single person has their birthday today is p 1 365 00274 If birthdays are independent then X number having a birthday today is a binomial random variable with n 72 and p 00274 Use Minitab to assist in answering the following a What is the probability that nobody among the n 72 students has a birthday today That is find P X 0 for a binomial random variable with n 72 and p 00274 b What is the probability one or more students among the n 72 students has a birthday today