Exam2_Review_Sp23

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Stat2332, Spring 23 Exam2 Review Dr Estacio-Hiroms These questions have been provided for your practice. Do not expect similar questions in the exam that you will take. Ch. 10-15: Probability Rules, Listing the Ways, Counting Techniques and Probability Distributions – Binomial, Geometric, Poisson and Exponential . StatCrunch version Questions 1 - 3: The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown in the table. 1. Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer had a medium level of satisfaction and used the company more than five times per month? A) 1/28 B) 81/140 C) 59/140 D)16/35 2. Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer did not have a medium level of satisfaction with the company? A) 5/7 B) 11/35 C) 2/7 D) 24/35 3. A customer is chosen at random. Given that the customer uses the company less than two times per month, what is the probability that the customer expressed low satisfaction with the company? A) 1/40 B) 41/70 C) 1/70 D) 1/2 Questions 7 - 10: Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. 4. What is the probability that a randomly chosen manager has earned exactly one college degree? A) 7/40 B)51/160 C) 33/40 D)81/160 5. What is the probability that a randomly chosen manager has earned at least one college degree? (college degree or higher) A) 7/40 B)51/160 C) 33/40 D)81/160 6. If we randomly selected one manager from this company, find the probability that he or she has an advanced (Master's or Ph.D.) degree and is a good manager. A) 2/160 B) 2/51 C) 2/39 D)39/160 7. What is the probability that a randomly chosen manager is a good managers or has an advanced degree? A) 45/80 B)22/40 C) 1/80 51/160 8. Given that a manager is rated as fair, what is the probability that this manager has high school degree? A) 1/160 B)1/12 C)1/87 D) 7/39 9. Are the events “HS degree” and “poor Manager Rating” independent events? A) Yes, because P(HS degree and Poor rating) = P(HS degree) * P(Poor rating)

B) No, because P(HS degree and Poor rating) ≠ P(HS degree) * P(Poor rating) C) Yes, because P(HS degree or Poor rating) = P(HS degree) + P(Poor rating) - P(HS degree and Poor rating D) No, because P(HS degree and Poor rating) = P(HS degree) * P(Poor rating) Questions 10 – 14: A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). 10. Find the probability that a randomly selected student, who is a sophomore, drives a foreign automobile. A) 65/110 B) 45/350 C) 65/350 D) 65/205 11. Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile. A) 65/110 B) 45/350 C) 65/350 D) 65/205 12. What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile? A) 230/350 B) 215/350 C) 15/205 D) 15/350 13. Which of the following events listed would be considered mutually exclusive events? A) The student is a junior and the student drives a domestic automobile B) The student is a junior and the student is a freshman C) The student is a senior and the student drives a domestic automobile. D) The student is a freshman and the student drives a foreign automobile 14. Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile. A) 10/35 B) 15/205 C) 15/350 D) 25/35 15. If P ( A ∣ B ) = 0 and P ( A ) ≠ 0, then which statement is false? A) Events A and B are mutually exclusive. B) Events A and B are independent. C) Events A and B have no sample points in common. D) Events A and B are dependent. 16. (Round to 3 decimal points). It is estimated that 45% of people in Fast-Food restaurants order a diet drink with their lunch. Find the probability that the fourth person orders a diet drink. A) 0.041 B) 0.959 C) 0.925 D) 0.075 17. License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? A) 456,976 B) 10,000 C) 6760 D) 67,600 18. How many different 5-digit sequences can be formed using the digits 0, 1,...,6 if repetition of digits is allowed? A) 30 B) 7776 C) 360 D) 16,807 19. Mark can remember only the first 4 digits of his friend's phone number. He also knows that the number has 7 digits and that the last digit is not a 0. If Mark were to dial all of the possible numbers and if it takes him 22 seconds to try each one, how long would it take to try every possibility? A) 366.7 minutes B) 330 minutes C) 36.7 minutes D) 11 minutes 20. How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? A) 343 B) 6 C) 5 D) 210

21. A musician plans to perform 4 selections. In how many ways can she arrange the musical selections? A) 4 B) 120 C) 16 D) 24 22. A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 39% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution? A) No, a binomial distribution requires only two possible outcomes for each experimental unit sampled. B) Yes, the sample size is n = 20. C) Yes, the sample is a random and independent sample. D) No, the employees would not be considered independent in the present sample. 23. For a binomial distribution, which probability is not equal to the probability of 1 success in 5 trials where the probability of success is .4? A) the probability of 4 failures in 5 trials where the probability of failure is .6 B) the probability of 4 failures in 5 trials where the probability of success is .4 C) the probability of 4 failures in 5 trials where the probability of success is .6 D) the probability of 1 success in 5 trials where the probability of failure is .6 24. It a recent study of college students indicated that 30% of all college students had at least one tattoo. A small private college decided to randomly and independently sample 15 of their students and ask if they have a tattoo. Find the probability that exactly 5 of the students reported that they did have at least one tattoo. A) 0.218 B) 0.722 C) 0.207 D) 0.515 25. In New York City at rush hour, the chance that a taxicab passes someone and is available is 15%. what is the probability that at least 10 cabs pass you before you find one that is free (before: success on 11 th attempt or later). A) 0.970 B) 0.803 C) 0.029 D) 0.197 26. A student takes a true-false test consisting of 10 questions. Assuming that the student guesses at each question, find the probability that the student answers exactly 8 questions correctly. A) 0.0439 B) 0.0352 C) 0.0264 D) 0.0176 27. Suppose you keep running an experiment until it is successful. Each run of the experiment has an 80% chance of being successful independently of other runs. The chance that your experiment is first successful on the 5th run is: A) 5 ( 0.80 ) 4 ( 0.20 ) because the number of times the experiment is ran follows a Binomial (n = 5; p = 0.20) distribution B) ( 0.80 ) 4 ( 0.20 ) because the number of times the experiment is ran follows a Geometric (p = 0.20) distribution C) ( 0.20 ) 4 ( 0.80 ) because the number of times the experiment is ran follows a Geometric (p = 0.80) distribution D) 5 ( 0.20 ) 4 ( 0.80 ) because the number of times the experiment is ran follows a Binomial (n = 5; p = 0.80) distribution 28. A totally unprepared student is taking a multiple-choice test with 25 problems. Each problem has four options, only one of which is the correct answer. The student attempts the problems one by one from the beginning and randomly chooses one option for each problem. The chance that his first correct answer occurs at or after Problem # 10 is: A) (3/4) 9 B) (3/4) 10 C) (1/4) 9 D) (3/4) 10 (1/4) 29. (Continuation) Suppose the student has attempted the first 2 questions and we know that he got none of those two questions correct. What is the chance that his first correct answer will occur 5 questions later (i.e., at the 7th question)? A) (3/4) 7 B) (3/4) 4 (1/4) C) (3/4) 5 (1/4) 2 D) (3/4) 7 (1/4) ( Questions 30 and 31) One ticket is drawn at random from each of the two boxes below:

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1 1 3 1 2 2 4 30. Find the chance that both numbers are odd numbers. a) 1/3 b) 1/6 c) 1/4 d) 1/2 31. Find the chance that at least one of the tickets is the ticket 1 . a) 3/4 b) 1/4 c) 2/3 d) 11/12 Originally from Exam01-Review: 32.The scatterplot below shows the relationship between the ages of women when they first married and the ages when they had their first child. The correlation coefficient between the values is 0.9315. The regression equation for the data is = 6.404 + 0.955 ∙ (Age-married) Would it be appropriate to say that the age at which a woman first marries causes her to have her first child after that age? a) No, since the correlation coefficient does not equal 1, we cannot conclude causation. b) Yes, since the correlation coefficient is close to 1, we can conclude causation. c) No, correlation never implies causation. d) Yes, the scatterplot shows a strong linear association, so the older a woman is when she first marries, the older she will be when she has her first child. 33. A random sample of 30 married couples were asked to report the height of their spouse and the height of their biological parent of the same gender as their spouse. The output of a regression analysis for predicting spouse height from parent height is shown. Assume that the conditions of the linear regression model are satisfied. What is the slope of the regression line? Choose the statement that is the correct interpretation of the slope in context. a) The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 48.40 inches taller, in the sample. b) The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample. c) The slope is 0.25. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample. d) The slope is 0.25. On average, for each 0.25 inches taller a parent is, the spouse is about 1 inch taller, in the sample. 34. Continuation. If the intercept was 0 and the slope was 1, what would that say about the association? a) It would mean that the spouse height should not be predicting using parent height. b) It would mean that on average, the spouse is 1 inch taller than the parent. c) It would mean that on average, the spouse and the parent are the same height. d) None of these. 35. Data were recorded for 117 months on a household's gas bill (in dollars) and the average monthly temperatures for its neighborhood. The mean monthly temperature was 48.7°F with a standard deviation of 20.6. The mean gas bill price was $81.20 with a standard deviation of 66.5. The correlation coefficient between monthly temperature and gas bill price is -0.92. Determine the correct value of the slope for the linear model that predicts gas bill price from monthly temperature and interpret it in context. a) The slope is -0.28. For every one dollar increase in gas bill price, the monthly temperature is predicted to decrease by 0.28°. b) The slope is -2.97. For every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $2.97. c) The slope is -2.97. For every one dollar increase in gas bill price, the monthly temperature is predicted to decrease by

2.97°. d) The slope is -0.28. For every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $0.28. 36. A regression line for predicting the selling prices of homes in Chicago is = 168 + 102x, where x is the square footage of the house. A house with 1500 square feet recently sold for $140,000. What is the residual for this observation? A) -13,000 B) -13,168 C) 13,168 D) 13,000 37. A regression line for predicting Internet usage (%) for 39 countries is where x is the per capita GDP, in thousands of dollars, and y is Internet usage. What is the residual for a country with a per capita GDP of $28,000 and actual Internet use of 38 percent? a) 1.79 b) 5.4 c) -1.79 d) -5.4 38. A regression line for predicting Internet usage (%) for 39 countries is where x is the per capita GDP, in thousands of dollars, and y is Internet usage. Interpret the residual for one of the 39 countries with per capita GDP of $15,000 and actual Internet use of 20 percent. a) The actual Internet usage for this country is 0.36% lower than expected from the regression equation. b) The actual Internet usage for this country is 3.6% higher than expected from the regression equation. c) The actual Internet usage for this country is 0.36% higher than expected from the regression equation. d) The actual Internet usage for this country is 3.25% lower than expected from the regression equation. ---------------------------------------------------------------------------------------------------------------------------------------------------- KEYS 1. A 2. D 3. A 4. D 5. C 6. A 7. B 8. C 9. B 10. A 11. C 12. B 13. B 14. A 15. B 16. D 17. D 18. D 19. B 20. D 21. D 22. A 23. C 24. C 25. D 26. A 27. C 28. A 29. B 30. C 31. A 32. C 33. C 34. C 35. B 36. B 37. C 38. C

Exam2_Review_Sp23

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