Using references to relevant theories, concepts about gradient of the line and its correlation, probability, estimation of the mean, and standard deviation, write an assignment of 2000 words by answering the following. Question 1 Discuss the procedure how to calculate the gradient of a line and the correlation between the independent and dependent variables given an equation of a line in the slope-intercept form. Question 2 Discuss the concept of the basic probability theory and the formula for probability. Apply the formula by providing at least two examples to calculate probability. Question 3 The following table gives the age group for 80 persons in a glee club. No. of persons (f) Age group 10 S 20 20 S 30 ? 30 s 40 ? 40 < 50 16 50 S 60 ? 60 S 70 ? 70 S 80 Ef=80 From the table above A. Prepare a table of values and calculate an estimate for the mean and standard deviation. B. Construct a histogram for the data above. C. Use the histogram to estimate the mode. Your report should contain the following: Introduction: Introduction which will include the overview related to the concept of gradient of a line, probability, estimation of the mean, and standard deviation.(200 words equivalent) Solution and Discussion Solution and discussion in question one. Student needs to provide an equation of the line in slope- intercept form. Draw the graph of the equation using the y-intercept and its slope. The discussion of plotting the y-intercept and the value of the slope will trace/draw the line. The inclusion of the calculation of the gradient using any two points is a must to verify the nature of the inclination of the line. (400 words equivalent) Solution and discussion in question two. Student needs to give the meaning of the basic probability theory as well as the probability formula. It is important to include at least two examples to calculate probability using the probability formula. The discussion of the calculation should be included. (500 words equivalent) Solution and discussion in question three. Student needs to provide the table of values to be able to calculate the mean and the standard deviation. Furthermore, the student needs to provide frequency density data to be able to construct histogram and to estimate the mode. The discussion of the completion of the table of values, construction of the histogram and the estimation of the mode should be included. (700 words equivalent) Conclusion Student needs to summarise the key points in the discussion. (200 words equivalent) ***END OF ASSIGNMENT TASK***