Statistics for Managerial Decision Making: Quiz 3 Insights

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 1/12 Quiz 3 - Results Attempt 1 of 1 Written Jan 30, 2024 6:38 PM - Jan 30, 2024 7:55 PM Attempt Score 94.57 / 100 - 94.57 % Overall Grade (Highest Attempt) 94.57 / 100 - 94.57 % Question 1 (Mandatory) 2.571 / 6 points Select all VALID probabilities values. Hide ques±on 1 feedback 1.01 50/49 -0.25 110% 0% 49/50 1 A probability can be any value between 0 (impossible) and 1 (certain)

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 2/12 Question 2 (Mandatory) 6 / 6 points Is a good hitter in baseball who has struck out the last six times due for a hit his next time up? Question 3 (Mandatory) 6 / 6 points Answer: 729 Hide ques±on 3 feedback A probability can be any value between 0 (impossible) and 1 (certain) A probability, the relative frequency of an event or outcome, can be any value between 0 (impossible) and 1 (certain) A probability, the relative frequency of an event or outcome, can be any value between 0 (impossible) and 1 (certain) This is an example of the Law of Averages. Yes, the hitter is now due for a hit. The Law of Large Numbers predicts the hitter is not due for a hit. The Law of Large Numbers predicts the hitter is due for a hit. This is an example of the so-called Law of Averages. No, the hitter is not due for a hit because the Law of Averages is non-existent and doesn't predict anything. How many sequences of 3 things can be formed from 9 different things with replacement and order is important? Note that a permutation or combination problem is sampling without replacement.

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 3/12 Question 4 (Mandatory) 6 / 6 points Answer: 720 Hide ques±on 4 feedback Question 5 (Mandatory) 6 / 6 points Answer: 6 Hide ques±on 5 feedback Question 6 (Mandatory) 8 / 10 points When drawing with replacement and order is important, Y X sequences of X things can be formed from Y different things. How many permutations can be formed by sampling 5 things from 6 different things? When drawing without replacement and order is important, =PERMUT(Y, X) permutations can be formed by sampling X things from Y different things How many combinations of 5 people can be formed from 6 people? =COMBIN (Y, X) committees of X people can be formed from Y people. This is sampling without replacement and order does not matter.

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1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 4/12 A local zoo has only mammals and reptiles. So, the sample space for this zoo has mammals and reptiles. Choose the statements when one animal is selected randomly. Question 7 (Mandatory) 6 / 6 points Toss 2 dice, and let the event be the sum of the values of the top faces. The possible outcomes are listed inside the following table at the intersection of the row of the "toss of 1st die" and the column of "toss of 2nd die": Because there are 36 outcomes, the probability of a sum = frequency of the sum/36. The probabilities of the sums are: Sum Probability 2 1/36 3 2/36 4 3/36 5 4/36 P(Mammal and Reptile) < 0 P(Mammal and Reptile) = 0, or impossible P(Mammal and Reptile) > 0, or possible P(Mammal or Reptile) = 0, or impossible P(Mammal or Reptile) = 1, or certain

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 5/12 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36 Only one of the sums 2 through 12 can occur in a single toss of the dice. These are mutually exclusive events. The Simple Addition Rule P(A or B) = P(A) + P(B applies). Match the items on the left to the items on the right. __ 2__ __ 3__ __ 1__ 1 . 2 . 3 . Hide ques±on 7 feedback Question 8 (Mandatory) 6 / 6 points What is the probability of choosing a red card or a King from a deck of 52 cards? 0.889 0.000 0.583 P(X at least 7) P(X is not 9) P(X = 1) P(X at least 7) = P(7) + P(8) + P(9) + P(10) + P(11) + P(12). The possible sums are mutually exclusive. The Simple Addition Rule applies. P(X is not 9) = 1 - P(9). The Complement Rule applies. P(X = 1) = 0 because 1 is not a possible sum.

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 6/12 Hide ques±on 8 feedback Question 9 (Mandatory) 6 / 6 points Events A and B occur sequentially. P(A) = 0.500 P(B) = 0.200 P(A and B) = 0.100, which means sometimes A and B occur jointly. Are events A and B independent? True False Hide ques±on 9 feedback Question 10 (Mandatory) 6 / 6 points General Multiplication Rule: P(A and B) = P(A) x P(B | A) Simple Multiplication Rule: P(A and B) = P(A) x P(B) Simple Addition Rule: P(A or B) = P(A) + P(B) General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B) Applies to a single trial where the possible events are not mutually exclusive (can occur jointly) P(A) x P(B) = 0.5 x 0.2 = 0.1 = P(A and B).

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1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 7/12 When are events A and B dependent? Question 11 (Mandatory) 6 / 6 points Two customers enter a store. Independently, they make decisions to purchase or not to purchase. The following diagram shows how the sequence of Customer 1 and Customer 2 decisions can combine to form the events of 0, 1, or 2 purchases, labeled on the right. So, each path left-to-right is a sequence of independent events. Which rule applies to a sequence of independent events? P(A and B) > 0, and P(A and B) ≠ P(A) x P(B) P(A and B) = 0 P(A and B) = P(A) x P(B)

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 8/12 Hide ques±on 11 feedback Question 12 (Mandatory) 6 / 6 points Simple Addition Rule: P(A or B) = P(A) + P(B) General Addition Rule: P(A or B) = P(A) + P(B) - P(A and B) General Multiplication Rule: P(A and B) = P(A) X P(B | A) Simple Multiplication Rule: P(A and B) = P(A)*P(B) Simple Multiplication Rule applies to a sequence of independent trials. Assume the following probabilities: P(Customer makes a purchase) = 0.150 P(Customer does not make a purchase) = 1- 0.150 Compute the probability of 0 purchases (neither customer purchases) and enter your answer with 3 decimal places.

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fro… 9/12 Answer: 0.723 Hide ques±on 12 feedback Question 13 (Mandatory) 6 / 6 points Answer: P(0 purchases) = P(Customer1 does not purchase and Customer 2 does not purchase) = P(Customer1 does not purchase) x P(Customer2 does not purchase)= Assume the following new probabilities: P(Customer makes a purchase) = 0.800 P(Customer does not make a purchase) = 1- 0.800 Compute the P(1 purchase) and enter your answer with 3 decimal places.

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1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fr… 10/12 0.320 Hide ques±on 13 feedback Question 14 (Mandatory) 6 / 6 points Answer: 0.244 Hide ques±on 14 feedback Use the Simple Multiplication Rule to get P(0 purchases) and P(2 purchases). P(0 purchases) = P(Cust1 does not purchase) x P(Cust2 does not purchase) = P(no purchase) x P(no purchase). P(2 purchases) = P(Cust1 purchases) x P(Cust2 purchases) = P(purchase) x P(purchase). 1 = P(0 purchases) + P(1 purchase) + P(2 purchases). P(1 purchase) = 1 - P(0 purchases) - P(2 purchases). Assume patients arrive at an emergency room independently with outcomes emergency or not emergency. If the probability of an emergency is 0.58, what is the probability of the event an emergency followed by a non-emergency? Round your computation to three decimal places. If the probability for an emergency is X, then the probability that it is not an emergency is 1-X. The answer is X * (1-X)

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fr… 11/12 Question 15 (Mandatory) 6 / 6 points Joint probabilities were determined to be P(Male) is a ______ probability. Hide ques±on 15 feedback Question 16 (Mandatory) 6 / 6 points Answer: Conditional Joint Marginal The sum of the values in a column or in a row is a marginal probability. P(Male) = P(Male and Republican) + P(Male and Democrat) + P(Male and Independent), which is the sum of values in the first row. Republican Democrat Independent Female 0.002 0.015 0.109 Male 0.014 0.125 ? Given the joint probabilities above, compute the probability of Democrat and enter your answer with 3 decimal places.

1/30/24, 7:56 PM Daniel Annunziata - MGMT 650 9046 Statistics for Managerial Decision Making (2242) - UMGC Learning Management System https://learn.umgc.edu/d2l/lms/quizzing/user/quiz_submissions_attempt.d2l?isprv=&qi=2119143&ai=12801106&isInPopup=0&cfql=0&fromQB=0&fr… 12/12 0.140 Hide ques±on 16 feedback Done Add the probability of female Democrats to the probability of male Democrats to get the marginal probability of event Democrat.

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