ACMS 10140_E2_S24

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May 6, 2024

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ACMS 10140 Multiple Choice Answer Grid – Exam 2 – Spring 202 4 Instructions: • Students must submit the grid with their exam to receive credit for the multiple choice questions. • Clearly 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) • 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. Use the following probability density function for a random variable X to answer questions 1 and 2. 1. Find P(8 ≤ X ≤ 20). A. 0.7500 B. 0.5625 C. 0.6250 D. 0.6875 2. Find the 40 th percentile value for X, i.e., find the value of k where P(X ≤ k) = 0.4 A. 7.2 B. 8.4 C. 9.2 D. 6.4 Use the following information to answer questions 3 - 4. A recent study of fast food restaurants found that Taco Bell had the quickest service with an average service time of 2.2 minutes from the time of the order. Assume that the service time for Taco Bell has an exponential distribution. 3. You just placed your order at Taco Bell. What is the probability that the service time will be less than 1 minute? A. 0.8892 B. 0.3653 C. 0.2885 D. 0.6347 4. Suppose a customer will receive a coupon for a free taco on their next visit if their food does not arrive within 6 minutes. What is the chance that this will happen for a randomly selected customer? A. 0.0844 B. 0.0297 C. 0.3667 D. 0.0654 2 4 6 8 10 12 14 16 18 x f(x)

5. The Central Limit Theorem tells us that A. 𝑋𝑋 � is approximately normally distributed only when the population distribution of X is normally distributed. B. 𝑝𝑝′ is approximately normally distributed only when the population distribution is normally distributed. C. 𝑝𝑝′ is approximately normally distributed when n is sufficiently large (n ≥ 30). D. 𝑋𝑋 � is approximately normally distributed when n is sufficiently large (n ≥ 30). 6. Which of the following statements is NOT true? A. All Normal distributions are bell-shaped and symmetric. B. All Uniform random variables can only take on non-negative values. C. All Exponential distributions are right-skewed. D. All continuous distributions have probability density functions with f(x) ≥ 0. Use the following information to answer questions 7 - 10. Worldwide, screen time has been found to be normally distributed with an average of 6.5 hours per day with a standard deviation of 1.25 hours per day. 7. What is the probability that a randomly selected person will have a screen time between 5 and 7 hours? A. 0.4719 B. 0.5404 C. 0.6247 D. 0.5763 8. Find the 97 th percentile value for screen time, in hours. A. 8.85 hours B. 7.71 hours C. 9.35 hours D. 8.97 hours 9. What value of screen time (in hours) is 1.6 standard deviations below the mean? A. 5.25 hours B. 4.9 hours C. 4.5 hours D. None of the above 10. Suppose that a random sample of 25 individuals was taken. What is the chance that their average screen time exceeds 7 hours? A. 0.1586 B. 0.3446 C. 0.2119 D. 0.0228

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