I need help with a math document. Please show all working out as well. Not just the answers.

Introduction to Statistics This PERFORMANCE ASSESSMENT TASK is designed to assess the learner's ability to calculate the measures of central tendencies, plot the five-number summary, construct relative frequency chart for a set of data, calculate basic probability, and determine whether there is a positive, negative or no linear relationship between two variables. Part I - Measures of Central tendency/Relative Frequency/ the Five-number Summary A random sample of 25 College students was asked, "How many hours per week typically do you work outside the home?" Their responses were as follows: (0, 0, 15, 20, 20, 40, 30, 20, 35, 35, 28, 15, 20, 25, 25, 30, 5, 10, 30, 34, 28, 30, 35, 15, 25} a. Find the mean, the median and the mode of hours worked outside the home for the sample data. Show all your work to justify your answer. b. Use the above data to complete the following table summarizing the number of hours worked outside the home. Express the relative frequency as a percent. Class Tally Frequency Relative Frequency (0-10) (11-20) (21 - 30) (31-40) Total c. Find the five-number summary of the hours worked outside of the home by the 25 College students. Show all your work to justify your answer. Part II- Basic Probability Consider the experiment of tossing two fair dice, and observing the sum of the two dice. a. Make a list of all possible outcomes.b. What is the probability that the sum of the two dice equals 8? State specifically what outcomes show a sum of two dice equals 8. c. What is the probability that the sum of the two dice equals 13? State specifically what outcomes show a sum of two dice equals 13. d. What is the probability that the sum of the two dice greater than 10? State specifically what outcomes show a sum of two dice greater than 10. e. What is the probability that the sum of the two dice is less than 1? State specifically, if any, what outcomes show a sum of two dice is less than 1. Part III- Linear Relationship Scenario: A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects eleven 3-year old children from her practice, measures their heights and head circumference, and obtains the data shown below: Height (inches) Head Circumference (inches) 27.75 17.5 24.5 17.1 25.5 17.2 26 17.3 25 16.9 25.75 17.6 26.5 17.3 27 17.5 26.75 17.3 26.75 17.6 27.5 17.5 a. If the pediatrician wants to use height to predict head circumference, determine which variable is the explanatory variable and which is response variable. b. Draw a scatter diagram of the data. c. Draw the best fit line on the scatter diagram. d. Does this scatter diagram show a positive, negative, or no relationship between a child's height and the head circumference? Note: The rubric for this Performance Assessment Task is on the following page. 2