BMGT 230 Midterm 2 Sample Exam PDF

BMGT 230: Business Statistics SAMPLE EXAM 2 BMGT 230: Business Statistics Sample Exam 2 Name: _________________________________ Section: _______________ UID: __________________...

BMGT 230: Business Statistics SAMPLE EXAM 2 BMGT 230: Business Statistics Sample Exam 2 Name: _________________________________ Section: _______________ UID: __________________________________ Please read and sign the following statement before you begin: I pledge on my honor that: o I will not give or receive unauthorized assistance during this exam. This includes, but is not limited to, communicating with anyone except the instructor or TAs, using unauthorized materials, or accessing external information. o I will not attempt to cheat or engage in any other form of academic dishonesty o I will follow all exam procedures o I will report any instances of cheating or academic dishonesty that I observe By signing this statement, I acknowledge that I have read and understand the above pledge and agree to abide by it. Signature: __________________________________________ Date: ________________ Instructions: During the actual exam, you may write on exam, the formula sheet, or the scratch paper. During the actual exam, you will enter your answers on a bubble sheet At the end of the exam, you will turn in the bubble sheet as well as the exam, scratch paper, and formula sheet. You may not leave the room with any exam materials. Once the exam begins, you may not leave the room until you are finished with the exam. Please make sure to use the bathroom before the exam starts. Do not wear ear buds, earphones, or smart watches during the exam. Your phone should be turned off or in “do not disturb” mode, and it should be put away (i.e. not on your desk) Don’t forget to bring your calculator and some extra pens or pencils with you – everything else will be provided for you. 1  BMGT 230: Business Statistics SAMPLE EXAM 2 1. A random variable X has an expected value of 10 and a standard deviation of 3. Let Y = 2X + 2. What are the expected value and standard deviation of Y, respectively? o Expected value = 20, standard deviation = 6 o Expected value = 20, standard deviation = 12 o Expected value = 20, standard deviation = 36 o Expected value = 22, standard deviation = 6 o Expected value = 22, standard deviation = 12 o Expected value = 22, standard deviation = 36 Use the following information to answer questions 2 -5. The time it takes a student to finish an electronics test has a uniform distribution between 40 and 60 minutes. 2. Find the probability that a student will take less than 45 minutes to finish the test. a. 0.25 b. 0.5 c. 0.75 d. 1 3. What is the probability that it takes a student between 50 and 65 minutes to finish the test? a. 0.25 b. 0.5 c. 0.75 d. 1 4. What is the probability that it takes the student exactly 55 minutes to finish the test? a. 0.05 b. 0.9582 c. 0.0418 d. 0 5. What is the standard deviation of the time it takes to finish the test? a. 33.33 b. 5.774 c. 50 d. 7.071 Use the following to answer questions 6-9. Suppose that, historically, 60% of college students are sports fans. A sample of 8 students is to be selected. 6. Find the probability that exactly 8 students are sports fans. a. 1 b. 0.9832 c. 0.9899 d. 0.0168 7. Find the probability that 6 or fewer students are sports fans. a. 0.8936 b. 0.7682 c. 0.6846 d. 0.1064 e.0.2318 8. Find the probability that more than 5 students are sports fans. a. 0.5941 b. 0.6846 c. 0.3154 d. 0.4059 9. Find the standard deviation of the number of sports fans. a. 4.8 b. 2.19 c. 1.92 d. 1.39 2  BMGT 230: Business Statistics SAMPLE EXAM 2 Use the following to answer questions 10-14. Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 6 pounds and a standard deviation of 3 pounds. 10. What proportion of the dieters lost more than 10 pounds? a. 1.33 b. 0.0918 c. 0.9082 d. 0.0104 11. What proportion of dieters lost fewer than 3 pounds? a. 0.1587 b. 1 c. 0.8413 d. 0.9582 12. What is the probability that a dieter lost between 4 and 7 pounds? a. 1 b. 0.1587 c. 0.3779 d. 0.33 13. What proportion of the dieters gained weight? a. 0 b. 0.0228 c. -2 d. it cannot be determined 14. What is the cutoff for the 20% of dieters who lost the most weight? a. 7.74 pounds b. 3.48 pounds c. 8.52 pounds d. 12 pounds 15. As the size of the sample gets larger and larger, the standard error of the sample mean: a. Gets smaller and smaller b. Gets larger and larger c. Does not change d. It cannot be determined from the information given 16. Suppose that 100 items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a non-normal probability distribution with mean of 150 ounces and standard deviation of 30 ounces. Which of the following is true about the sampling distribution of x ? a. It has a mean of 150 ounces b. It has a standard error of 3 ounces c. It has an approximately normal distribution d. All of these choices are true 17. An unfair coin has a 70% probability of landing with heads face-up. The coin is tossed 8 times. What is the probability that there are 4 or fewer heads in the 8 tosses? a. 0.0580 b. 0.1941 c. 0.1361 d. 0.8059 e. 0.9420 3  BMGT 230: Business Statistics SAMPLE EXAM 2 18. For sample sizes greater than 50, the sampling distribution of the mean is approximately normally distributed: a. Regardless of the distribution of the population values b. Only if the shape of the population is symmetric c. Only if the population is normally distributed d. None of these choices 19. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 2.8 pounds and standard deviation of 0.64 pounds. If a sample of 49 fish is taken, what is the standard error of the mean weight? a. 0.64 b. 0.3024 c. 0.0914 d. None of these choices 20. For a sample size of 1, the sampling distribution of the mean is normally distributed: a. Regardless of the distribution of the population values b. Only if the shape of the population is symmetric c. Only if the population is normally distributed d. None of these choices 21. If a sample of size 50 is taken from a particular population, the probability that the sample mean is greater than 1 standard deviation above the mean is about 5%. If a sample of size 200 is taken from the same population, will the probability that the sample mean is greater than one standard deviation larger than the mean be the same, get larger, or get smaller? a. It will be the same b. It will get larger c. It will get smaller d. There is no way to tell (Use this info to answer questions 21 and 22) A sample of 49 retirees is drawn at random from a normal population whose mean age and standard deviation are 74 and 10.5 years, respectively. 22. What is the probability that the sample mean is between 71 and 75 years? a. 0.1539 b. 0.6687 c. 1 d. 0.9922 23. What is the probability that the sample mean age is greater than 72 years? a. 0.5753 b. 0.4247 c. 0.0918 d. 0.9082 4  BMGT 230: Business Statistics SAMPLE EXAM 2 (Use this info to answer questions 24 and 25) The proportion of pet owners who feed their pets human food is 60%. A random sample of 25 pet owners was taken. 24. What is the probability that, in the sample of 25 pet owners, more than 76% feed their pets human food? a. 0.0516 b. 0.8968 c. 0.9484 d. 0.0007 25. What is the probability that the sample proportion is within 5% of the population proportion? a. 0.51 b. 0.305 c. 0.39 d. 0.695 26. Under what circumstances can you use the central limit theorem to make inferences about the sample proportion 𝑝̅ ? a. If the population is normally distributed b. If the sample size is at least 30 c. If the sample size is large relative to the population proportion d. You can always use the central limit theorem e. If 𝑝(1 − p) > 5 27. The expected value of the sample mean is 𝐸(𝑋̅) = 𝜇. What property does this represent? a. Consistency b. Relative efficiency c. Unbiasedness d. Normal probability distribution Use this information to answer questions 28-29. When calling a certain bank, the length of time that customers must wait on hold before speaking to an agent has a continuous uniform distribution between 10 seconds and 1.5 minutes. 28. What is the probability that a randomly selected customer must wait on hold for longer than one minute? a. 0.625 b. 0.75 c. 0.375 d. 0.25 e. none of these 29. A random sample of 40 callers is taken and their hold times recorded. What is the probability that the average hold time is longer than one minute? a. 0.0031 b. 0.9969 c. 0.3336 d. 0 e. none of these 5  BMGT 230: Business Statistics SAMPLE EXAM 2 30. Indicate the type of sampling used: Janine wants to make sure that men and women are equally represented in her survey of UMD athletes. She first separates the athletes into men and women, and then takes a random sample from each group. a. Simple random sample b. Stratified sample c. Cluster sample d. Flash mob sample 31. The difference between a sample mean and a population mean is called: a. Sampling error b. Nonsampling error c. Nonresponse error d. Selection bias 32. Which of the following types of sampling is most appropriate if there is more variation within groups than between groups? a. Simple random sampling b. Stratified sampling c. Cluster sampling d. Survey sampling 33. A random sample of size 16 is taken from a population with mean 20 and variance 64. What is the probability that the sample mean is greater than 22? a. 0.1587 b. 0.8413 c. 0.4483 d. It cannot be determined from the information given 34. Which of the following is an example of nonsampling error? a. Incorrect responses of recorded b. Responses are not obtained from all members of the population c. There is a difference between the sample and the population d. All of these are true 35. A sample of size n is taken from a population with a normal distribution with mean 𝜇 and standard deviation 𝜎. Which of the following is true about the sampling distribution of the sample mean 𝑋̅? a. It is approximately normally distributed if n > 30 b. It has a standard error of 𝜎 2 /𝑛 c. It is always normally distributed, regardless of the sample size d. All of these are true 6  BMGT 230: Business Statistics SAMPLE EXAM 2 36. The weight of shipments in a warehouse is normally distributed with a mean of 100 kilograms and a variance of 400 kg. A sample of 100 shipments is taken every month and the average iscalculated. How much must the average shipment weigh to be in the 10% of heaviest average shipments? a. 102.6 kilograms b. 97.44 kilograms c. 125.6 kilograms d. 104.7 kilograms e. 146.7 kilograms Use the following information to answer questions 37-38 A psychiatrist believes that she can quantify the probability that a new patient will trust her. 20% of new patients trust her on the first visit, 15% of patients trust her on the second, 35% of patients trust her on the third, 20% trust her on the fourth, and the rest trust her on the fifth visit. 37. What is the probability it takes at least 4 visits to gain trust? a. 10% b. 20% c. 30% d. 40% 38. What is the average number of visits it takes for the psychiatrist to gain the trust of a new patient? a. 3 visits b. 2.85 visits c. 2.5 visits d. None of these answers are correct. 7  BMGT 230: Business Statistics SAMPLE EXAM 2 Use the following figure to answer questions 39-40. X is a random variable with the probability distribution shown below. The left side of the triangle is at 0.1 and the right side is at 0.6. 39. What is the height of the triangle, in order for the probability distribution to be valid? a. 4 b. 2 c. 1 d. 0.4 e. None of these 40. What is the probability that X is less than 0.45? a. 0.7 b. 0.3 c. 0.91 d. 0.09 e. 0.86 8