41. A pair of dice is thrown. Let Z₁ be the number shown on the first die and Z₂ be the number shown on the second die. Let X = Z₁ + Z₂ and Y = Z₁ Z₂. Find a. E(Z₁). b. E(Z2). c. E(X).

The Quick Sell car dealership has been using 1-minute spot ads on a local TV station. The ads always occur during the evening hours and advertise the different models and price ranges of cars on the lot that week. During a 10-week period, the Quick Sell dealer kept a weekly record of the number x of TV ads versus the number y of cars sold. The results are given in Table below. . ( Show your work--No work no credit) x y 6 15 20 31 0 10 14 16 25 28 16 20 28 40 18 25 10 12 8 15 Draw a scatter diagram for the data ( You can copy and past this graph in your work area by using any technology). Do you see a linear relation? Compute the value of linear correlation coefficient "r". From the value of "r" can we decide the strength of the relation ( strong, moderate, or weak)? Find the equation of regression line, identify the slope and intercept. Also explain  meaning  of slope in the context of the problem. How many cars can the manager expect to sell if 12 ads per…

I roll two dice and observe two numbers X and Y. If Z = X - Y, find... a. the range of Z b. the PMF oz Z

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Running Shoes. A shoe designer tests a new material for the soles of their most popular line of running shoes. She has 6 athletes run 100 miles with one of last years shoes and one of these new shoes, randomly assigning the new shoe to the left or right foot. Afterward, she measures the amount of wear on each of the shoes in millimeters. Test the claim that the amount of wear with the new material is different from the amount of wear with the old material. Runner 4 1 2 3 1.14 1.04 1.08 1.09 New Material Wear Old Material Wear 1.03 0.87 0.96 1.01 (b) Write the hypotheses in symbols. Ho: Hdiff-new-old = 0 Ha: Hdiff-new-old > 0 O Ho: Pdiff-new-old (a) Why are these paired data? O The top and bottom values in each column are from the same runner. Runners typically run in groups of two. There are an equal number of shoes of each type. This table does not have paired data; there is no clear relationship between the top and bottom values in any column. Each runner has a pair of shoes. -0 Ha:…

the following diagram. hew 3h- FASTRAC k etermine the value of h. Determine the value of k.

H.: µ = 47.6 and H, : µ < 47.6 where u = the mean age of teachers at Ravenwood High School. The calculated p-value is 0.023. What conclusion will you make at a = 0.10? O Reject the H. O Fail to reject the H. O Reject the H. O Fail to reject the Ha

The spinner shown is spun once. Deteremine... P(blue) RED GREEN GREEN 8. 1 4. ame YELLOW BLUE 1/2 15

A researcher wants to determine if the exam scores of the students are dependent on the length of time spent in studying the subject. Ten students in a certain class were taken and the results are shown in the table below where X is the time spent in studying the subject in hours and Y is the examination scores. X (time) Y (score) 1.5 80 3.0 83 1.25 83 0.5 70 3.5 85 2.5 75 1.0 70 3.0 90 2.5 86 4.0 91 Determine the simple linear regression equation Y = a + bX. (round off values up to 1 decimal place)