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

Instructions:Your initial post will include five screen shots and four sentences (one sentence for each of the last four screen shots).Screenshot #1Flip a coin. Your flip will determine the trigonometric function you will be working with for your initial post.Heads = use sineTails = use cosineFor example, if I flipped a tail, my initial post would focus on the trigonometric function cosine.Graph your function and take a screen shot of the graph.You can use any program you like. Here is one option: Illuminations: Trigonometric Graphing.Please refer to the discussion board on how to take screen shots.Graph  y=cos(x) ory=sin(x) Your subject line will be cos(x) or sin(x) depending on your flip.Screenshot #2Now, consider this equation. The equation used will depend on your original coin toss.y=Acos(B(x−C))+D y=Asin(B(x−C))+DUsing the Illuminations: Trigonometric Graphing site, figure out what happens when you make A larger (try 1, 2, 3, and 4).Explain in one sentence what happens as you make A larger and tell us what this transformation is called.Then pick an interesting large number (something larger than 1), and graph y=Acos(x)  or  y=Asin(x)The equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Screenshot #3Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make B larger (try 1, 2, 3, and 4) and tell us what this transformation is called.Explain in one sentence what happens as you make B larger.Then pick an interesting large number (something larger than 1), and graph y=cos(Bx)  or  y=sin(Bx)The equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Screenshot #4Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make C larger (try 0, 30 degrees, 45 degrees, and 60 degrees) and tell us what this transformation is called.Explain in one sentence what happens as you make C larger.Then pick an interesting large number (something larger than 0), and graph y=cos(x+C) y=sin(x+C)The equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Screenshot #5Using the Illuminations: Trigonometric Graphing site, figure out what happens when you make D larger (try 0, 1, 2, and 3) and tell us what this transformation is called.Explain in one sentence what happens as you make D largerThen pick an interesting large number (something larger than 0), and graph y=cos(x)+D or y=sin(x)+DThe equation used will depend on your original coin toss.Take a screen shot of your graph and post the equation.Response Post:Pick another student’s post who flipped their coin opposite of you.For my example, I would pick someone who flipped heads, or has sin(x) in their subject line.Review the other student’s post.Does each of their answers make sense to you?Explain in at least two sentences why or why not their post makes sense.Please be respectful of other students’ work.Pick two of their transformations (meaning A, B, C, or D and the corresponding graph).What happens when you change the transformation from a positive value to a negative value? For example, if you picked A and D, what happens when you change equations to: y=−Acos(x)  or y=−Asin(x)Remember, find the Trig function opposite of yours.What happens when you change the equation to: y=cos(x)−D  or y=sin(x)−DPost a screen shot of both transformations together: y=−Acos(x)−D  or  y=−Asin(x)−D