ACMS10140_E1_F23

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Apr 3, 2024

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ACMS 10140 Multiple Choice Answer Grid – Exam 1 - Fall 2023 Instructions: • Students must submit the grid with their exam to receive credit for the multiple choice questions. • Neatly write your response (A, B, C, or D) to each item in the response box for that item. • Use UPPERCASE letters only. • Graders will NOT look at the circled answers on the actual questions. No exceptions. • All pages of the exam must be submitted. Name (print neatly): ____________________________________________________________________ Item Response Item Response Item Response Item Response 1 6 11 16 2 7 12 17 3 8 13 18 4 9 14 19 5 10 15 20

Part I: Multiple Choice Questions (50 points) - Exam 1 - Fall 2023 • There are 20 questions. Each question is worth 2.5 points. • You must enter your answers (A, B, C, D) in the Answer Grid provided (last page of exam). • Graders will NOT look at the circled answers on the actual questions. No exceptions. 1. A company has developed a new battery, but the average lifetime is unknown. In order to estimate the average, a sample of 100 batteries is randomly tested, and the average lifetime of this sample is found to be 250 hours. The variable of interest is A. the sample of 100 batteries B. the lifetime of the new battery C. all batteries produced by the company D. 250 hours 2. The best graphical method to summarize qualitative data is a A. bar graph B. histogram C. stem-and-leaf plot D. box plot 3. Which symbol is used to represent the population standard deviation? A. x B. s C. µ D. σ 4. Which of the following measurements is considered to have a nominal scale? A. T-shirt size (S, M, L, XL, XXL) B. Number of siblings (0, 1, 2, 3, …) C. Temperature (Freezing, Cool, Neutral, Warm, Hot) D. Political party preference (1=Democrat, 2=Republican, 3=Independent, 4=Other) 5. A population A. is the same as a sample. B. is the selection of a random sample. C. is the collection of all items of interest in a particular study. D. always has the same size as the sample. 6. Some hotels ask their guests to rate their services as poor(1), average(2), good(3), or excellent(4). Hotel rating (on a scale from 1 to 4) is an example of a A. qualitative ordinal variable B. qualitative nominal variable C. quantitative discrete variable D. quantitative continuous variable 7. Which of the following is not an example of a discrete random variable? A. Number of customers who place an order by phone B. Number of defective items in a shipment of 50 items C. Number of times “tails” occurs in 10 tosses of a fair coin D. Age of a randomly selected Notre Dame student when 1000 are sampled

Use the following plot to answer questions 8 – 10. The following stem-and-leaf plot shows the number of patients attended by a house physician in 21 randomly selected weeks. (key: 1 | 8 = 18 patients) 1 8 8 8 9 9 9 2 4 4 4 4 6 8 8 8 9 3 0 1 2 2 4 0 1 8. What is the mode of the data? A. 18 B. 19 C. 24 D. 28 9. For how many weeks did the physician attend to between 19 and 31 patients, inclusive? A. 14 B. 13 C. 12 D. 11 10. The median number of patients is A. 26 B. 25 C. 27 D. 28 11. If events A and B are mutually exclusive, then A. they must be independent. B. the sum of their probabilities, P(A) + P(B), must be equal to one. C. the sum of their probabilities, P(A) + P(B), must be equal to P(A or B). D. the product of their probabilities, P(A)P(B), must be equal to P(A and B). 12. The probability assigned to each experimental outcome must be A. any value greater than zero. B. any value smaller than zero. C. at least one. D. between zero and one, inclusive. 13. On a December day at Notre Dame, the probability of snow is 0.30. The probability of a cold day is 0.50. The probability of a cold and snowy day is 0.15. Are cold and snow independent events? A. Yes, since P(cold and snow) = P(cold)P(snow) B. No, since P(cold and snow) ≠ P(cold)P(snow) C. Yes, since P(cold or snow) = P(cold) + P(snow) D. No, since P(cold or snow) ≠ P(cold) + P(snow) 14. Let 𝑨𝑨′ be the complement of event A . Then, 𝑷𝑷 ( 𝑨𝑨 ) + 𝑷𝑷 ( 𝑨𝑨 ′ ) = A. 0.0 B. 0.5 C. 1.0 D. More information is needed.

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Use the probability distribution table below for questions 15-16. 15. Find P(X=40). A. 0.20 B. 0.25 C. 0.15 D. 0.10 16. Find the expected value of X. A. 27 B. 30 C. 34 D. 39 Use the following to answer questions 17– 18. Fifty-five percent of applications for a credit card are accepted. Assume that the decision made on any application is independent of all other decisions previously made. Assume that X = number of applications accepted out of five has a binomial distribution. 17. What is the chance that all of the next five applications are rejected? A. 0.5500 B. 0.1128 C. 0.0185 D. 0.0503 18. What is the chance that at least two applications are accepted out of five? A. 0.7438 B. 0.8688 C. 0.2756 D. 0.5981 Use the following to answer questions 19 – 20. On average, 3 cars arrive at the drive-up window of a bank every thirty minutes. Define the Poisson random variable X to be the number of cars arriving in any thirty minute interval. 19. Find the probability that fewer than 2 cars arrive in a thirty minute interval. A. 0.2240 B. 0.1494 C. 0.4232 D. 0.1991 20. What is the probability of at least one arrival in a one hour interval? A. 𝑒𝑒 −3 B. 1 − 𝑒𝑒 −3 C. 𝑒𝑒 − 6 D. 1 − 𝑒𝑒 −6 x 10 20 30 40 50 60 P(X=x) 0.05 0.20 0.30 ?? 0.15 0.05

Part II: Written Problems (50 points) • For all parts, you must show work. Answers without accompanying work will not receive full credit. • Write all final answers in the boxes provided. • Write your final answers as either exact fractions or rounded to three decimal places. 1. (20 points) A random sample of 200 individuals reported their email provider and cell phone provider. Email Provider Cell Phone Provider AT&T Verizon Sprint Total Gmail 33 17 7 57 Yahoo 36 31 10 77 Other 26 24 16 66 Total 95 72 33 200 A. (4 points) Estimate the probability that a randomly selected individual uses Yahoo as their email provider. B. (4 points) Estimate the probability that a randomly selected individual uses Yahoo their email provider and AT&T as their cell phone provider. C. (4 points) Given that an individual uses Gmail as their email provider, estimate the probability that they use Verizon as their cell phone provider. D. (4 points) Estimate the probability that a randomly selected individual uses “Other” as their email provider or Sprint as their cell phone provider. E. (2 points) Are Email Provider and Cell Phone Provider independent? (Circle one) Yes / No F. (2 points) Which probability method was used to estimate these probabilities? (Circle one) Classical Empirical Subjective

2. (30 points) A random sample of 20 students took a ten question True/False quiz worth 10 points. The histogram below gives a summary of the students’ scores (X = number of correct answers out of 10). A. (8 points) Using the data shown in the histogram, fill in the table below. Quiz Score, X Frequency Relative Frequency Percent Frequency (%) B. (4 points) Calculate the sample mean quiz score for the 20 students. Answer C. (4 points) Calculate the sample v ariance for the quiz scores for the 20 students. Note that ∑ 𝒙𝒙 𝒊𝒊 𝟐𝟐 = 𝟏𝟏𝟏𝟏𝟐𝟐𝟏𝟏 𝟐𝟐𝟐𝟐 𝒊𝒊=𝟏𝟏 . Answer 0 1 2 3 4 5 6 7 8 9 10 5 6 7 8 9 10 Frequency Quiz Score

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Continued from previous page D. (3 points) Calculate the median quiz score for the 20 students. Answer E. (5 points) Calculate the interquartile range (IQR) for the 20 students. Answer F. (2 points) Provide the mode quiz score for the 20 students. Answer G. (2 points) What type of variable is X = Quiz Score? Circle all that apply. Qualitative Quantitative Nominal Ordinal Discrete Continuous H. (2 points) The distribution shape for this data set is (circle one): left-skewed symmetric right-skewed uniform bimodal

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