UIZ 2 Name___________________________________ STAT 200; INTRODUCTION TO STATISTICS; SPRING 2017 Due by 11:59pm EDT SUNDAY Please answer all 16 questions. The maximum score for the quiz is 80 points (All questions are equally weighted). Make sure your answers are as complete as possible and show your work/argument. In particular, when there are calculations involved, you should show how you come up with your answers with necessary tables, if applicable. Answers that come straight from program software packages will not be accepted. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work Be sure to show answers on the answer sheet provided. IMPORTANT: Per the direction of the Dean's Office, you are requested to include a brief note at the beginning of your submitted quiz, confirming that your work is your own. By typing my signature below, I pledge that this is my own work done in accordance with the UMUC _________________________ Electronic Signature Your submitted quiz will be accepted only if you have included this statement. Use the empirical rule to solve the problem. 1 1. The systolic blood pressure of 18- year- old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18- year- old women have a systolic blood pressure between 96 mmHg and 144 mmHg? Determine which score corresponds to the higher relative position. 2. Which score has the highest relative position: a score of 32 on a test for which x = 26 and s = 10, a score of 5.7 on a test for which x = 4.7 and s = 1.3 or a score of 394.5 on a test for which x = 374 and s = 41? Find the indicated probability. 3. Refer to the table which summarizes the results of testing for a certain disease. Positive Test Result Negative Test Result Subject has the disease 120 4 Subject does not have the disease 13 172 If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? What does this probability suggest about the accuracy of the test? 2 4. The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. Waiting Time Number of (minutes) Customers 0-3 11 4-7 9 8 - 11 11 12- 15 5 16- 19 5 20- 23 1 24- 27 3 If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes? 5. 100 employees of a company are asked how they get to work and whether they work full time or part time. The figure below shows the results. If one of the 100 employees is randomly selected, find the probability that the person drives alone or cycles to work. 1. Public transportation: 9 full time, 8 part time 2. Bicycle: 3 full time, 4 part time 3. Drive alone: 32 full time, 28 part time 4. Carpool: 9 full time, 7 part time 3 6. You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction. Find the indicated probability. Round to the nearest thousandth. 7. A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 8. The table below shows the soft drinks preferences of people in three age groups. cola root beer lemon- lime under 21 years of age 40 25 20 between 21 and 40 35 20 30 over 40 years of age 20 30 35 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age given that they drink root beer. Solve the problem. 9. How many ways can an IRS auditor select 5 of 10 tax returns for an audit? 10. How many 5 - digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is not allowed? 4 Answer the question. 11. If an apple is hanging from a string and three flies land on it, find the probability that all three are on points that are within the same hemisphere. 12. If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)? 13. Fifty students took an Introduction to Chemistry exam. Assume that their scores formed a normal distribution with a mean of 80 and standard deviation of 4. The professor decided to adjust the scores by creating z scores. Only the first 2.5% of students got an A. Students were curious what actual scores would be A's? 5 14. Consider a multiple-choice test with ten questions. Each question has five answer choices, and only one answer is correct. If someone picks answers purely by guessing (at random), find the probability of obtaining 80% or better purely by guessing. 15. The mean weight, , of the US population is 140 lbs. with a standard deviation, , of 22 lbs. What will be the minimum weight of the top 80 percentile? 16. Compute the 99% confidence interval of the population mean when the sample mean is 214, the sample standard deviation is 63, sample size is 49. 6