exam1a with ans

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School

Arizona State University *

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Course

380

Subject

Chemistry

Date

Feb 20, 2024

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pdf

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Uploaded by CoachTankSheep35

iee380 - 2023fall - exam1a Turn in only the Scantron sheet to any proctor. Keep the scrap sheet and the question sheet. All questions are multiple choice; select just one answer for each question. Fill in the letter of your answer choice on the Scantron in pencil. Unless otherwise directed, compute all numerical values to four decimal places using conventional rounding methods. For example, 3.14159 to four decimal places is 3.1416. If you do not see your answer as one of the choices, select “Answer not here” if it is one of the choices. 1. This is exam version A. We want you to remember which version you have so we are going to ask a pretty simple question here: Which exam version do you have? a a. A b. B c. C d. D e. E 2. If , what is the derivatives of with respect to ? d ?(𝑥) = 7 𝑥 2 ?(𝑥) 𝑥 a. b. c. d. e. 14 𝑥 2 7 𝑥 3 − 14 𝑥 2 − 14 𝑥 3 14 𝑥 3 3. If f(x) = 6x, then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x = 4 and x = 7? a a. 99 b. 81 c. 117 d. 144 e. 121 4. A digital scale is used that provides weights to the nearest gram. The sample space for this experiment is S={0,1,2,3,...}. Let A denote the event that a weight exceeds 11 grams, let B denote the event that a weight is less than or equal to 15 grams, and let C denote the event that a weight is greater or equal to 8 grams and less than 12 grams. Find . e ? ∪ (? ∩ ?) a. {0, 1, 2, ...,7} b.{8, 9, 10, 11} c.Ø d. S e.{8, 9, 10, ...} 5. If S is the sample space of a random experiment and E is any event, the axioms of probability are: d a. P(S) = 1 b. 0 ≤ P(E) c. For any two events 𝐸 1, 𝐸 2 with 𝐸 1∩ 𝐸 2= ∅ , 𝑃 ( 𝐸 1 ∪𝐸 2)= 𝑃 ( 𝐸 1)+ 𝑃 ( 𝐸 2) d. All of the choices are correct e. None of the choices is correct 6. Determine the value of P(A|B) + P(A'|B) b a. 0 b. 1 c. 2 d. -1 e. None of the choices is correct 7. If a sample space consists of N possible outcomes that are equally likely, the corresponding random variable follows which distribution? c a. Normal distribution b. Poisson distribution c. Discrete uniform distribution d. Continuous uniform distribution e. Exponential distribution 8. Let C be the event that a student received a grade of B or better in Calculus I and let S be event that a student received a grade of A in Statistics I. Which of the following denotes the probability that a student received an A in statistics given that the student received less than a B grade in Calculus I. d a. P(S|C) b. P(S'|C') c. P(C|S) d. P(S|C') 9. Determine the value of a 𝑛 2 ( ) a. n(n-1)/2 b. n/2 c. 0 d. 1 e. n+1

10. If P(A|B) = 0.49, P(B) = 0.75 and P(A) = 0.49, which of the following is correct? c a. A and B are independent b. A’ and B are independent c. All of the choices are correct D. None of the choices is correct 11. The probability that a lab specimen contains high levels of contamination is 0.12. A group of 4 independent samples are checked. Round your answers to four decimal places (e.g. 0.9876). What is the probability that none contain high levels of contamination? e a. 0.2597 b. 0.4261 c. 0.3075 d. 0.4751 e. 0.3271 12. (Based on the previous question) What is the probability that exactly one contains high levels of contamination? b a. 0.3975 b. 0.4003 c. 0.5251 d. 0.6751 e. 0.8214 13. A group of 1,000 people are tested for a gene called Ifi202 that has been found to increase the risk for lupus. The random variable is the number of people who carry the gene. Determine the range (possible values) of the random variable. d a. {1, 2, ..., 1000} b. {0, 1, ..., 999} c. {1, 2, ..., 1001} d. {0, 1, ..., 1000} 14. Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.14, 0.15, 0.16, 0.17, 0.18. Determine the mean of the coating thickness for this process. c a. 0.14 b. 0.15 c. 0.16 d. 0.17 e. 0.18 15. (Based on the previous question) Determine the variance of the coating thickness for this process. b a. 0.0001 b. 0.0002 c. 0.0003 d. 0.0004 e. 0.0005 16. A scientist used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.61. What is the probability of more than 1 death in a corps in a year? a a. 0.1252 b. 0.1167 c. 0.2435 d. 0.0426 e. 0.3474 17. Suppose that for . What is the value of P(1<X<2.5)? e ?(𝑥) = ? −𝑥 𝑥 > 0 a. 0.3679 b. 0.1245 c. 0.4217 d. 0.1546 e. 0.2858 18. Suppose that for . Determine the value of such that is a pdf. c ?(𝑥) = ? 𝑥 0 < 𝑥 < 𝑘 𝑘 ?(𝑥) a. 0 b. 1 c. 0.6931 d. 1.2411 e. ∞ 19. Assume X is normally distributed with a mean of 10 and a standard deviation of 2, determine P(6 < X < 14) . b a. 0.8759 b. 0.9545 c. 0.6894 d. 0.5528 e. 0.9981 20. Assume X is normally distributed with a mean of 9 and a standard deviation of 2. Determine the value for x where P(x<X<9)=0.2. Round the answers to 2 decimal places. a a. 7.95 b. 6.75 c. 8.21 d. 8.59 e. 6.02

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