2. The Standard Normal Distribution can be described as a. N(0,1) b.n(1,0)

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1 Practice Questions for Exam 1 Questions 1-4 General Questions 1.Find P(Z> 1.48). a b c d e.none of the above 2. The Standard Normal Distribution can be described as a. N(0,1) b.n(1,0) c.n(µ, σ) d.n(µ, σ 2 ) 3. The probability density function for a continuous random variable is f(x) = -2x+c for 0<x<1. Find the value of c. a.-1 b. 2/3 c. 1 d.2 e. Can not be determined 4. The probability function for a continuous random variable is f(x) = 2x for o<x<1. Find the expected value. a. 2/3 b. 1 c. Can not be determined because you need the probability of each point

2 Questions 5-7Civil engineers help municipal wastewater treatment plants operate more efficiently by collecting data on quality of the affluent. On seven occasions, the amounts of suspended solids (parts per million) at one plant were described in the stem and leaf plot below. Stem-and-leaf of C1 N = 7 Leaf Unit = (3) Find the mean. a. 2.6 b.2.8 c.28 d.26 e.none of the above 6. Find the standard deviation. a b c d Find the median. a. 2.6 b.21 c.26 d.326 Question 8 General Question 8. Let X denote the distance(m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for white tailed deer, X has an Exponential Distribution with parameter λ = What is the probability that the deer moves less than 100m? a b c d

3 Question 9-10 Upon reviewing recent usage of conference rooms at an engineering consulting firm, an industrial engineer determined the following function for the number of requests for a conference room per half day. The function is listed below. X f(x) Which of the following descriptions adequately identifies the function? a. This is a probability mass function for a discrete random variable. b. This is a cumulative probability function for a discrete random variable. c. This is a probability density function for a continuous random variable. d. This is a cumulative probability function for a continuous random variable. 10. F(2)= a.0.2 b.0.45 c.0.67 d.0.78 Questions During one stage in the manufacturing of integrated circuit chips, a coating must be applied. After each application the chips have to be examined to determine if the coating is complete. In the past, 30% of the chips receive a complete coating. The remaining chips must be recoated Let X= the number of chips that have a complete coating. You decide to sample 10 chips. 11. The following condition is not necessary for the above situation to be a Binomial distribution: a. You must have n independent trials b. You probability of success, p, must not change from trial to trial. c. You must draw chips until you get one chip that is not completely coated. d. The trials must be independent of each other. 12. Assuming that X has a Binomial Distribution, what is the variance of chips that have a complete coating? a.2.1 b.3 c.7 d Assuming that X has a Binomial Distribution, what is the probability that 2 chips have a complete coating? a. 0 b c d

4 Questions The probability that a communication system will have high fidelity(f) and high selectivity(s) is The probability that it will have high selectivity(s) is The probability that is has high fidelity(f) is What is the probability that the communication system with high fidelity will also have high selectivity? a.0.18 b.0.22 c.0.81 d e.none of the above 15. The options of high fidelity and high selectivity must be a. complimentary b. mutually exclusive c. independent d. none of the above 16. What is the probability that the communication system has high fidelity or high selectivity or both? a b c d Questions Match the following probability distributions with the descriptions of X below. A. Exponential B. Poisson C. Binomial 17. The average number of machine failures in a plant is believed to be 2 per 24 hour day. Let X= the number of machine failures in the plant during the next day. 18. During peak hours, customers arrive at a supermarket checkout counter at a rate of 2 per minute. Let X=time before arrival of the next customer 19. A student takes a multiple choice oral examination, where each questions has 5 choices of which one is correct. The student was too busy to attend class or to study for the exam. So, he has to guess the answer to each questions. The grade on the test is decided by X=the number of correct answers.

5 Questions If the amount of cosmic radiation to which a person is exposed while flying by jet across the United States is a random variable having a Normal Distribution with mean =4.35 mrem and standard deviation =0.59 mrems. 20. What is the probability that a person is exposed to more than 4.2 mrems of radiation? a b c d e.none of the above 21. If a person receives radiation at the 98 th percentile of all those that travel across the United States, how much radiation did the person receive? a. less than b c d What percentage of travelers is exposed to between 3.17 and 5.53 mrems of radiation? a. 68% b. 78% c. 90% d. 95% 23. In what type of distributions is the median bigger than the mean? a. right skewed b. left skewed c. symmetric d. bimodal 24. If you look at individuals over the age of 18, 45% of the 18 to 25 age group use group chat, 22% of the 26 to 36 age group use group chat and 10% of those over 36 use group chat. It has also been found that 29% of adult users of the Internet are between 18 and 25, 47% are between 26 and 36, and 24% are over 36. What percent of all adult users of the Internet take part in group chat? a.) 26% b.) 31% c.) 59% d.) 100%

6 25. The probability that any one of the incandescent lights in Norman Hall is not working is There are 12 lights in Norman Hall. Assume that the lights are independent. What is the probability that all of the lights are working? a. 1.0 x 10^-12 b c d. None of the above 26. A description of different houses on the market includes the following three variables. Which of the variables is quantitative? a.) The square footage of the house b.) The monthly gas bill. c.) The monthly electric bill. d.) All of the above. Answers 1. A 2. A 3. D 4. A 5. C 6. B 7. C 8. D 9. A 10. C 11. C 12. A 13. D 14. D 15. D 16. D 17. B 18. A 19. C 20. C 21. E 22. D 23. B 24. A 25.D 26. D