MidtermThere are 8 questions in total, each worth 12.5 points. Please upload your answers to the dropbox. The Grantham Late policy applies to the midterm, and it is a 5% deduction per late day. Remember that work is required. That work may be calculations, a computer printout, an Excel program - but there has to be something that shows where numbers came from. This midterm may only be taken one time. Question 1The following shows the temperatures (high, low) and weather conditions in a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy.Is “condition” an element, variable, or observation?Provide the observation for Mexico City.Give an example of a quantitative variable.Provide the range for the low temperature.What is the mode for the high temperature?Explain why the "lo" is not ordinal. Question 2A student has completed 16 courses in the School of Arts and Sciences. Her grades in the 16 courses are shown below.DDCDABFAAACBBCCDDevelop a frequency distribution table for her grades.Create a bar chart for her grades. Remember the importance of good titles and labeled axes.All the courses are three credits except for the two that are highlighted. They are science courses and are worth 5 credits each. Using a weighted mean, calculate the student's grade point average. A = 4.0; B= 3.0; C= 2.0; D =1.0; F = 0 Question 3The number of hours worked per week for a sample of ten students is shown below.StudentHours1332403154255156307328109151035Determine the mean, median, and mode.Explain which of the three values (mean, median, mode) is the best representation of central tendency in this particular set of data. (This is not an "in general" question.)What is the standard deviation for the number of hours worked? What does standard deviation tell us?Create a histogram for this data. Discuss whether or not this data is normally distributed. Justify your answer. Question 4You are given the following information on Events A, B, C, and D.P(A) = .5P(B) = .3P (C) = .20P(A U D) = .8P(A ∩ C) = 0.05P (A │B) = 0.22P (A ∩ D) = 0.25Compute P(D).Compute P(A ∩ B).Compute P(A | C).Compute the probability of the complement of C.What does it mean to be mutually exclusive? Give an example. Question 5When a particular machine is functioning properly, 80% of the items produced are non-defective. If seven items are examined, what is the probability that three are defective?If seven items are examined, what is the probability at at least three are non-defective?If seven items are examined, what is the probability that at most, one is defective?What is the expected number of defective items if ten items are examined? Question 6The average starting salary of this year’s graduates of a large university (LU) is $34,000 with a standard deviation of $7,000. Furthermore, it is known that the starting salaries are normally distributed.What is the probability that a randomly selected LU graduate will have a starting salary of at least $32,000?Individuals with starting salaries of less than $19,900 receive a low income tax break. What percentage of the graduates will receive the tax break?What percent of graduates will have their salaries one standard deviation from the mean?What is the range of salaries that is one standard deviation from the mean? What is the range of salaries that are two standard deviations from the mean? Question 7A simple random sample of 8 computer programmers revealed the sex of the programmers and the following information about their weekly incomes.ProgrammerWeekly IncomeSexA$550MB$654MC$911FD$500ME$727MF$688FG$1000FH$892MIf all the salaries were written on separate pieces of paper, and one was drawn at random, what is the probability that the one that was drawn would be over $700?If a programmer were selected at random to complete a project, what would the probability be that the programmer was male?What is the probability of selecting an income of under $700 per week given that a male was selected?If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that both were female?If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that the first draw would be the salary of a male and the second would be one of a female? Question 8Students of a large university spend an average of $7 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 25 students is taken.What is the probability that the sample mean will be at least $4?Jason spent $15 on his lunch. Explain, in terms of standard deviation, why his expenditure is not usual.Explain what information is given on a z table. For example, if a student calculated a z value of 2.77, what is the four-digit number on the z table that corresponds with that value? What exactly is that 4-digit number telling us?Explain why we use z formulas. Why don't we just leave the data alone? Why do we convert?Grading Criteria AssignmentsMaximum PointsMeets or exceeds established assignment criteria40Demonstrates an understanding of lesson concepts20Clearly presents well-reasoned ideas and concepts30Uses proper mechanics, punctuation, sentence structure, and spelling10Total100

Week 5: Consumer MathematicsEveryone benefits from effective money management. Money is earned, bills are paid, and savings accounts are created. But what happens when the money you earn is not enough to cover your immediate needs or wants? This is where a loan comes in.No matter how much money you make in your lifetime, it is likely that at some point you will take out a loan. This could be for education, a home, a car, or a hobby, such as a boat. If you have taken out a loan, you already know there is a cost for taking that loan. How much of that loan is interest, or money paid to the financial institution for lending you the cash? How much of your monthly payment is paying down the debt, and how much is paying interest on that amount? If you haven't taken out a loan before, you will be glad to work through this math now so that you are prepared for the true costs involved.This week, you will explore the math behind finances, loans, and interest payments. You also re-examine your own personal financial management techniques.Discussion: Repaying LoansBefore taking out a loan, it is important to know the repayment terms and how your interest rate and the time of the loan affect the total loan balance.For this Discussion, you examine the effect of simple and compound interest, as well as time on the principal balance of a loan. You also explore how these variables affect loan repayment.To prepare for this Discussion:Think of a big-ticket item you might need to take out a loan to purchase. Dream big. What have you always wanted? This could be a boat, car, motorcycle, a trip around the world, etc. Research the cost of this item.Select a reasonable interest rate for your item (between 2% and 10% is standard).Select a time period to pay off your loan (between 3 and 10 years is commonPost at least 2 paragraphs in response to the following:Paragraph 1:Describe the item you are taking a loan out for and the purchase price.Include your chosen interest rate and amount of time for your loan.Determine the amount of interest you will pay throughout the term of the loan and the final cost of the item when the loan is paid in full. Note: Assume your bank uses the simple interest formula: Interest = Principal * Rate * Time.Show the work needed to find the amount of interest and total cost.Determine the monthly payment for this loan.Paragraph 2:Repeat the interest computation however lower the time frame by one year. Show your work.Determine the total amount of the loan when paid in full.Compute the new monthly payment.Explain if you are surprised by the results. Why, or why not?Discuss one change you could make in your life to make the new monthly payment possible.